๐’๐ˆ๐๐†๐˜๐„ ๐’๐ญ๐ฎ๐๐ข๐จ
๐’๐ˆ๐๐†๐˜๐„ ๐’๐ญ๐ฎ๐๐ข๐จ
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๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ญ(๐ฑ) = - ๐œ๐จ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
6:42
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ญ๐š๐ง(๐ฑ) = ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
6:29
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ฌ(๐ฑ) = - ๐ฌ๐ข๐ง(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
5:04
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ฌ๐ข๐ง(๐ฑ) = ๐œ๐จ๐ฌ(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
6:29
๐ˆ๐๐ค ๐ฐ๐ก๐š๐ญ ๐ˆ๐ฆ ๐๐จ๐ข๐ง๐  ๐ฐ๐ซ๐จ๐ง๐  | ๐‘๐ž๐๐๐ข๐ญ | ๐๐ฎ๐š๐๐ซ๐š๐ญ๐ซ๐ข๐œ ๐Ÿ๐ฎ๐ง๐œ๐ญ๐ข๐จ๐ง๐ฌ
14:09
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ
15:12
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ฌ๐ž๐œ(๐ฑ) = ๐ฌ๐ž๐œ(๐ฑ)๐ญ๐š๐ง(๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
In this video, I proof the result: derivative of sec(x) is sec(x)tan(x) from the first principle. Although this result is fundamental, only few knows why this is true.
#bhutan #dailyconcepts #mathematics #reddit #calculus
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Links(my other videos and blog):
Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ
Researchgate: www.researchgate.net/profile/Singye-Wangchuk-7
Visit my Blog: physicswithsingye.blogspot.com/
LinkedIn: in.linkedin.com/in/singye608
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Previous Videos:
Standard Model of particles: ua-cam.com/video/kPQwpRVEqls/v-deo.html
CMB: ua-cam.com/video/3h3gQZb_Moo/v-deo.html
Facts about Universe: ua-cam.com/video/eWQ6c-X0PlE/v-deo.html
Bjuchu Thangka Dema: ua-cam.com/video/gi5uB0idSBk/v-deo.html
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My resources:
1. Video editing software I use: Davinci Resolve 18, VN Editor
(check out Google AppStore and apple store)
2. Animation software I use: krita
krita.org/en/download/krita-desktop/
3. Photos and music: Royalty free photos and music (check websites)
Free footage: www.pexels.com/
4. Writing and editing tech I use: iPad Air(4th gen), Macbook Air M2
5. Camera I use: oppo f15, ipad air4
Instagram: singye__608
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0:00 Intro to first principle
0:56 Start of the proof
1:20 Expansion using double angle formula for sin(x) and cos(x)
3:53 Recalling important limit result and evaluating
4:36 Result
5:29 Outro
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ะŸะตั€ะตะณะปัะดั–ะฒ: 4

ะ’ั–ะดะตะพ

๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ญ(๐ฑ) = - ๐œ๐จ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ6:42๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ญ(๐ฑ) = - ๐œ๐จ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ญ(๐ฑ) = - ๐œ๐จ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 4
In this video, I proof the result: derivative of cot(x) is - cosec^2(x) from the first principle. Although this result is fundamental, only few knows why this is true. #bhutan #dailyconcepts #mathematics #reddit #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ Researchgate: www.researchgate.net/profile/Singy...
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ญ๐š๐ง(๐ฑ) = ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ6:29๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ญ๐š๐ง(๐ฑ) = ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ญ๐š๐ง(๐ฑ) = ๐ฌ๐ž๐œ^๐Ÿ (๐ฑ) | ๐๐ซ๐จ๐จ๐Ÿ | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 4ะ”ะตะฝัŒ ั‚ะพะผัƒ
In this video, I proof the result: derivative of tan(x) is sec^2(x) from the first principle. Although this result is fundamental, only few knows why this is true. #bhutan #dailyconcepts #mathematics #reddit #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ Researchgate: www.researchgate.net/profile/Singye-Wa...
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ฌ(๐ฑ) = - ๐ฌ๐ข๐ง(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ5:04๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ฌ(๐ฑ) = - ๐ฌ๐ข๐ง(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐œ๐จ๐ฌ(๐ฑ) = - ๐ฌ๐ข๐ง(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
ะŸะตั€ะตะณะปัะดั–ะฒ 18ะ”ะตะฝัŒ ั‚ะพะผัƒ
In this video, I proof the result: derivative of cos(x) is -sin(x) from the first principle. Although this result is fundamental, only few knows why this is true. #bhutan #dailyconcepts #mathematics #reddit #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ Researchgate: www.researchgate.net/profile/Singye-Wan...
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ฌ๐ข๐ง(๐ฑ) = ๐œ๐จ๐ฌ(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ6:29๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ฌ๐ข๐ง(๐ฑ) = ๐œ๐จ๐ฌ(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž ๐จ๐Ÿ ๐ฌ๐ข๐ง(๐ฑ) = ๐œ๐จ๐ฌ(๐ฑ) | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ | ๐๐ซ๐จ๐จ๐Ÿ
ะŸะตั€ะตะณะปัะดั–ะฒ 11ะ”ะตะฝัŒ ั‚ะพะผัƒ
In this video, I proof the result: derivative of sin(x) is cos(x) from the first principle. Although this result is fundamental, only few knows why this is true. #bhutan #dailyconcepts #mathematics #reddit #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ Researchgate: www.researchgate.net/profile/Singye-Wang...
๐ˆ๐๐ค ๐ฐ๐ก๐š๐ญ ๐ˆ๐ฆ ๐๐จ๐ข๐ง๐  ๐ฐ๐ซ๐จ๐ง๐  | ๐‘๐ž๐๐๐ข๐ญ | ๐๐ฎ๐š๐๐ซ๐š๐ญ๐ซ๐ข๐œ ๐Ÿ๐ฎ๐ง๐œ๐ญ๐ข๐จ๐ง๐ฌ14:09๐ˆ๐๐ค ๐ฐ๐ก๐š๐ญ ๐ˆ๐ฆ ๐๐จ๐ข๐ง๐  ๐ฐ๐ซ๐จ๐ง๐  | ๐‘๐ž๐๐๐ข๐ญ | ๐๐ฎ๐š๐๐ซ๐š๐ญ๐ซ๐ข๐œ ๐Ÿ๐ฎ๐ง๐œ๐ญ๐ข๐จ๐ง๐ฌ
๐ˆ๐๐ค ๐ฐ๐ก๐š๐ญ ๐ˆ๐ฆ ๐๐จ๐ข๐ง๐  ๐ฐ๐ซ๐จ๐ง๐  | ๐‘๐ž๐๐๐ข๐ญ | ๐๐ฎ๐š๐๐ซ๐š๐ญ๐ซ๐ข๐œ ๐Ÿ๐ฎ๐ง๐œ๐ญ๐ข๐จ๐ง๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 1214 ะดะฝั–ะฒ ั‚ะพะผัƒ
In this video, I solve one question that I came across on reddit on quadratic functions. Here, I use geometric and analytical proof for maxima using the second derivative test. Such an interesting question. #bhutan #dailyconcepts #mathematics #reddit #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWIsAAAAJ Researchg...
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ15:12๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ
ะŸะตั€ะตะณะปัะดั–ะฒ 8521 ะดะตะฝัŒ ั‚ะพะผัƒ
In this video, I derive the proof of ๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[๐ฌ๐ข๐ง๐ฑ/๐ฑ] & ๐ฅ๐ข๐ฆ[๐Ÿ-๐œ๐จ๐ฌ๐ฑ/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ geometrically and using Squeeze Theorem. This result of limit is essential to differentiate functions involving trigonometry. This is part 2 of the video. #bhutan #dailyconcepts #mathematics #calculus #limits Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&...
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ6:09๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[{๐ฌ๐ข๐ง๐ฑ}/๐ฑ] & ๐ฅ๐ข๐ฆ[{๐Ÿ-๐œ๐จ๐ฌ๐ฑ}/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ | ๐๐š๐ซ๐ญ ๐Ÿ | ๐†๐ž๐จ๐ฆ๐ž๐ญ๐ซ๐ข๐œ๐š๐ฅ ๐๐ซ๐จ๐จ๐Ÿ
ะŸะตั€ะตะณะปัะดั–ะฒ 3321 ะดะตะฝัŒ ั‚ะพะผัƒ
In this video, I derive the proof of ๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ฅ๐ข๐ฆ[๐ฌ๐ข๐ง๐ฑ/๐ฑ] & ๐ฅ๐ข๐ฆ[๐Ÿ-๐œ๐จ๐ฌ๐ฑ/๐ฑ] ๐ฐ๐ก๐ž๐ง ๐ฑ ๐ ๐จ๐ž๐ฌ ๐ญ๐จ ๐ŸŽ geometrically and using Squeeze Theorem. This result of limit is essential to differentiate functions involving trigonometry. This is part 1 of the video. #bhutan #dailyconcepts #mathematics #calculus #limits Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&...
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐๐ฎ๐จ๐ญ๐ข๐ž๐ง๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ10:45๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐๐ฎ๐จ๐ญ๐ข๐ž๐ง๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐๐ฎ๐จ๐ญ๐ข๐ž๐ง๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 1321 ะดะตะฝัŒ ั‚ะพะผัƒ
In this video, I derive the proof of the quotient rule of differentiation from the first principle. Although we use this every time when we differentiate a function involving a quotient, only few cares to know why it works this way. #bhutan #dailyconcepts #mathematics #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7Mm...
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐๐ซ๐จ๐๐ฎ๐œ๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ8:15๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐๐ซ๐จ๐๐ฎ๐œ๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐๐ซ๐จ๐๐ฎ๐œ๐ญ ๐‘๐ฎ๐ฅ๐ž ๐จ๐Ÿ ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 1621 ะดะตะฝัŒ ั‚ะพะผัƒ
In this video, I derive the proof of the product rule of differentiation from the first principle. Although we use this every time when we differentiate a function involving a product, only few cares to know why it works this way. #bhutan #dailyconcepts #mathematics #calculus Links(my other videos and blog): Google Scholar: scholar.google.com/citations?view_op=list_works&hl=en&hl=en&user=A7MmWI...
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐œ๐ก๐š๐ข๐ง ๐ซ๐ฎ๐ฅ๐ž | ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ7:55๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐œ๐ก๐š๐ข๐ง ๐ซ๐ฎ๐ฅ๐ž | ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐œ๐ก๐š๐ข๐ง ๐ซ๐ฎ๐ฅ๐ž | ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 3321 ะดะตะฝัŒ ั‚ะพะผัƒ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐ญ๐ก๐ž ๐œ๐ก๐š๐ข๐ง ๐ซ๐ฎ๐ฅ๐ž | ๐ƒ๐ข๐Ÿ๐Ÿ๐ž๐ซ๐ž๐ง๐ญ๐ข๐š๐ญ๐ข๐จ๐ง | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ž^{๐ฑ}]/๐๐ฑ=๐ž^{๐ฑ} | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ ๐๐š๐ฌ๐ข๐œ๐ฌ10:17๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ž^{๐ฑ}]/๐๐ฑ=๐ž^{๐ฑ} | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ ๐๐š๐ฌ๐ข๐œ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ž^{๐ฑ}]/๐๐ฑ=๐ž^{๐ฑ} | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ ๐๐š๐ฌ๐ข๐œ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 2121 ะดะตะฝัŒ ั‚ะพะผัƒ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ž^{๐ฑ}]/๐๐ฑ=๐ž^{๐ฑ} | ๐…๐ข๐ซ๐ฌ๐ญ ๐๐ซ๐ข๐ง๐œ๐ข๐ฉ๐ฅ๐ž | ๐‚๐š๐ฅ๐œ๐ฎ๐ฅ๐ฎ๐ฌ ๐๐š๐ฌ๐ข๐œ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ฅ๐ง(๐ฑ)]/๐๐ฑ=๐Ÿ/๐ฑ | ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž | ๐‹๐ข๐ฆ๐ข๐ญ๐ฌ12:32๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ฅ๐ง(๐ฑ)]/๐๐ฑ=๐Ÿ/๐ฑ | ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž | ๐‹๐ข๐ฆ๐ข๐ญ๐ฌ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ฅ๐ง(๐ฑ)]/๐๐ฑ=๐Ÿ/๐ฑ | ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž | ๐‹๐ข๐ฆ๐ข๐ญ๐ฌ
ะŸะตั€ะตะณะปัะดั–ะฒ 1628 ะดะฝั–ะฒ ั‚ะพะผัƒ
๐๐ซ๐จ๐จ๐Ÿ ๐จ๐Ÿ ๐[๐ฅ๐ง(๐ฑ)]/๐๐ฑ=๐Ÿ/๐ฑ | ๐ƒ๐ž๐ซ๐ข๐ฏ๐š๐ญ๐ข๐ฏ๐ž | ๐‹๐ข๐ฆ๐ข๐ญ๐ฌ
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘6:46๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘
ะŸะตั€ะตะณะปัะดั–ะฒ 26ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘9:46๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
ะŸะตั€ะตะณะปัะดั–ะฒ 17ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘3:27๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
ะŸะตั€ะตะณะปัะดั–ะฒ 28ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐๐จ๐ฌ๐ข๐ญ๐ข๐จ๐ง ๐š๐ง๐ ๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘| ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐Œ๐ž๐ญ๐ก๐จ๐6:08๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘| ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐Œ๐ž๐ญ๐ก๐จ๐
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘| ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐Œ๐ž๐ญ๐ก๐จ๐
ะŸะตั€ะตะณะปัะดั–ะฒ 19ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ‘/๐Ÿ‘| ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐Œ๐ž๐ญ๐ก๐จ๐
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง7:44๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
ะŸะตั€ะตะณะปัะดั–ะฒ 10ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง6:05๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
ะŸะตั€ะตะณะปัะดั–ะฒ 51ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐Š๐ข๐ง๐ž๐ฆ๐š๐ญ๐ข๐œ ๐„๐ช๐ฎ๐š๐ญ๐ข๐จ๐ง ๐จ๐Ÿ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž | ๐๐š๐ซ๐ญ ๐Ÿ/๐Ÿ‘ | ๐€๐ง๐š๐ฅ๐ฒ๐ญ๐ข๐œ๐š๐ฅ ๐’๐จ๐ฅ๐ฎ๐ญ๐ข๐จ๐ง
๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐š๐ง๐ ๐€๐œ๐œ๐ž๐ฅ๐ž๐ซ๐š๐ญ๐ข๐จ๐ง ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž12:04๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐š๐ง๐ ๐€๐œ๐œ๐ž๐ฅ๐ž๐ซ๐š๐ญ๐ข๐จ๐ง ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž
๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐š๐ง๐ ๐€๐œ๐œ๐ž๐ฅ๐ž๐ซ๐š๐ญ๐ข๐จ๐ง ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž
ะŸะตั€ะตะณะปัะดั–ะฒ 35ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐•๐ž๐ฅ๐จ๐œ๐ข๐ญ๐ฒ ๐š๐ง๐ ๐€๐œ๐œ๐ž๐ฅ๐ž๐ซ๐š๐ญ๐ข๐จ๐ง ๐๐ซ๐จ๐›๐ฅ๐ž๐ฆ | ๐Œ๐จ๐ญ๐ข๐จ๐ง ๐ข๐ง ๐’๐ญ๐ซ๐š๐ข๐ ๐ก๐ญ ๐‹๐ข๐ง๐ž
๐‹๐ž๐š๐ซ๐ง๐ข๐ง๐  ๐‚๐ฎ๐ซ๐ฏ๐ž | ๐ˆ๐ง๐๐ฎ๐ฌ๐ญ๐ซ๐ข๐š๐ฅ ๐„๐ง๐ ๐ข๐ง๐ž๐ž๐ซ๐ข๐ง๐ 15:36๐‹๐ž๐š๐ซ๐ง๐ข๐ง๐  ๐‚๐ฎ๐ซ๐ฏ๐ž | ๐ˆ๐ง๐๐ฎ๐ฌ๐ญ๐ซ๐ข๐š๐ฅ ๐„๐ง๐ ๐ข๐ง๐ž๐ž๐ซ๐ข๐ง๐ 
๐‹๐ž๐š๐ซ๐ง๐ข๐ง๐  ๐‚๐ฎ๐ซ๐ฏ๐ž | ๐ˆ๐ง๐๐ฎ๐ฌ๐ญ๐ซ๐ข๐š๐ฅ ๐„๐ง๐ ๐ข๐ง๐ž๐ž๐ซ๐ข๐ง๐ 
ะŸะตั€ะตะณะปัะดั–ะฒ 40ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐‹๐ž๐š๐ซ๐ง๐ข๐ง๐  ๐‚๐ฎ๐ซ๐ฏ๐ž | ๐ˆ๐ง๐๐ฎ๐ฌ๐ญ๐ซ๐ข๐š๐ฅ ๐„๐ง๐ ๐ข๐ง๐ž๐ž๐ซ๐ข๐ง๐ 
๐ƒ๐ฎ๐ง๐ง๐ข๐ง๐ -๐Š๐ซ๐ฎ๐ ๐ž๐ซ ๐„๐Ÿ๐Ÿ๐ž๐œ๐ญ8:13๐ƒ๐ฎ๐ง๐ง๐ข๐ง๐ -๐Š๐ซ๐ฎ๐ ๐ž๐ซ ๐„๐Ÿ๐Ÿ๐ž๐œ๐ญ
๐ƒ๐ฎ๐ง๐ง๐ข๐ง๐ -๐Š๐ซ๐ฎ๐ ๐ž๐ซ ๐„๐Ÿ๐Ÿ๐ž๐œ๐ญ
ะŸะตั€ะตะณะปัะดั–ะฒ 29ะœั–ััั†ัŒ ั‚ะพะผัƒ
๐ƒ๐ฎ๐ง๐ง๐ข๐ง๐ -๐Š๐ซ๐ฎ๐ ๐ž๐ซ ๐„๐Ÿ๐Ÿ๐ž๐œ๐ญ
๐€๐ซ๐ž๐š ๐ข๐ง ๐ญ๐ž๐ซ๐ฆ๐ฌ ๐จ๐Ÿ ๐ฉ๐ž๐ซ๐œ๐ž๐ง๐ญ๐š๐ ๐ž | ๐Œ๐š๐ญ๐ก | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’5:00๐€๐ซ๐ž๐š ๐ข๐ง ๐ญ๐ž๐ซ๐ฆ๐ฌ ๐จ๐Ÿ ๐ฉ๐ž๐ซ๐œ๐ž๐ง๐ญ๐š๐ ๐ž | ๐Œ๐š๐ญ๐ก | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐€๐ซ๐ž๐š ๐ข๐ง ๐ญ๐ž๐ซ๐ฆ๐ฌ ๐จ๐Ÿ ๐ฉ๐ž๐ซ๐œ๐ž๐ง๐ญ๐š๐ ๐ž | ๐Œ๐š๐ญ๐ก | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
ะŸะตั€ะตะณะปัะดั–ะฒ 282 ะผั–ััั†ั– ั‚ะพะผัƒ
๐€๐ซ๐ž๐š ๐ข๐ง ๐ญ๐ž๐ซ๐ฆ๐ฌ ๐จ๐Ÿ ๐ฉ๐ž๐ซ๐œ๐ž๐ง๐ญ๐š๐ ๐ž | ๐Œ๐š๐ญ๐ก | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐•๐ข๐ฅ๐ฅ๐š๐ ๐ž ๐‹๐ข๐Ÿ๐ž | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’1:08๐•๐ข๐ฅ๐ฅ๐š๐ ๐ž ๐‹๐ข๐Ÿ๐ž | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐•๐ข๐ฅ๐ฅ๐š๐ ๐ž ๐‹๐ข๐Ÿ๐ž | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
ะŸะตั€ะตะณะปัะดั–ะฒ 253 ะผั–ััั†ั– ั‚ะพะผัƒ
๐•๐ข๐ฅ๐ฅ๐š๐ ๐ž ๐‹๐ข๐Ÿ๐ž | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐…๐š๐ซ๐ž๐ฐ๐ž๐ฅ๐ฅ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’ | ๐ƒ๐“๐”_๐๐’๐€2:54๐…๐š๐ซ๐ž๐ฐ๐ž๐ฅ๐ฅ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’ | ๐ƒ๐“๐”_๐๐’๐€
๐…๐š๐ซ๐ž๐ฐ๐ž๐ฅ๐ฅ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’ | ๐ƒ๐“๐”_๐๐’๐€
ะŸะตั€ะตะณะปัะดั–ะฒ 676 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐…๐š๐ซ๐ž๐ฐ๐ž๐ฅ๐ฅ ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’ | ๐ƒ๐“๐”_๐๐’๐€
๐ƒ๐ž๐ง ๐‘๐š ๐ƒ๐ž๐ง ๐†๐š | ๐ƒ๐“๐” | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’0:50๐ƒ๐ž๐ง ๐‘๐š ๐ƒ๐ž๐ง ๐†๐š | ๐ƒ๐“๐” | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐ƒ๐ž๐ง ๐‘๐š ๐ƒ๐ž๐ง ๐†๐š | ๐ƒ๐“๐” | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
ะŸะตั€ะตะณะปัะดั–ะฒ 4287 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐ƒ๐ž๐ง ๐‘๐š ๐ƒ๐ž๐ง ๐†๐š | ๐ƒ๐“๐” | ๐Ÿ๐ŸŽ๐Ÿ๐Ÿ’
๐๐ ๐ฒ๐ข๐ง๐ญ๐ก๐ฎ๐ž๐ง ๐–๐š๐ง๐ ๐ฆ๐จ | ๐’๐ฅ๐จ๐ฐ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐ƒ๐“๐”0:59๐๐ ๐ฒ๐ข๐ง๐ญ๐ก๐ฎ๐ž๐ง ๐–๐š๐ง๐ ๐ฆ๐จ | ๐’๐ฅ๐จ๐ฐ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐ƒ๐“๐”
๐๐ ๐ฒ๐ข๐ง๐ญ๐ก๐ฎ๐ž๐ง ๐–๐š๐ง๐ ๐ฆ๐จ | ๐’๐ฅ๐จ๐ฐ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐ƒ๐“๐”
ะŸะตั€ะตะณะปัะดั–ะฒ 407 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐๐ ๐ฒ๐ข๐ง๐ญ๐ก๐ฎ๐ž๐ง ๐–๐š๐ง๐ ๐ฆ๐จ | ๐’๐ฅ๐จ๐ฐ ๐Œ๐จ๐ญ๐ข๐จ๐ง | ๐ƒ๐“๐”
๐–๐จ๐ซ๐ค ๐š๐ง๐ ๐’๐จ๐œ๐ข๐š๐ฅ ๐‹๐ข๐Ÿ๐ž ๐๐š๐ฅ๐š๐ง๐œ๐ž | ๐„๐ ๐Ÿ14:43๐–๐จ๐ซ๐ค ๐š๐ง๐ ๐’๐จ๐œ๐ข๐š๐ฅ ๐‹๐ข๐Ÿ๐ž ๐๐š๐ฅ๐š๐ง๐œ๐ž | ๐„๐ ๐Ÿ
๐–๐จ๐ซ๐ค ๐š๐ง๐ ๐’๐จ๐œ๐ข๐š๐ฅ ๐‹๐ข๐Ÿ๐ž ๐๐š๐ฅ๐š๐ง๐œ๐ž | ๐„๐ ๐Ÿ
ะŸะตั€ะตะณะปัะดั–ะฒ 937 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐–๐จ๐ซ๐ค ๐š๐ง๐ ๐’๐จ๐œ๐ข๐š๐ฅ ๐‹๐ข๐Ÿ๐ž ๐๐š๐ฅ๐š๐ง๐œ๐ž | ๐„๐ ๐Ÿ
๐๐ก๐ฎ๐ญ๐š๐ง๐ž๐ฌ๐ž ๐ƒ๐š๐ง๐œ๐ž | ๐ƒ๐“๐” ๐„๐ง๐ ๐ข๐…๐ž๐ฌ๐ญ '๐Ÿ๐Ÿ’ | ๐๐’๐€_๐ƒ๐“๐”3:37๐๐ก๐ฎ๐ญ๐š๐ง๐ž๐ฌ๐ž ๐ƒ๐š๐ง๐œ๐ž | ๐ƒ๐“๐” ๐„๐ง๐ ๐ข๐…๐ž๐ฌ๐ญ '๐Ÿ๐Ÿ’ | ๐๐’๐€_๐ƒ๐“๐”
๐๐ก๐ฎ๐ญ๐š๐ง๐ž๐ฌ๐ž ๐ƒ๐š๐ง๐œ๐ž | ๐ƒ๐“๐” ๐„๐ง๐ ๐ข๐…๐ž๐ฌ๐ญ '๐Ÿ๐Ÿ’ | ๐๐’๐€_๐ƒ๐“๐”
ะŸะตั€ะตะณะปัะดั–ะฒ 2498 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐๐ก๐ฎ๐ญ๐š๐ง๐ž๐ฌ๐ž ๐ƒ๐š๐ง๐œ๐ž | ๐ƒ๐“๐” ๐„๐ง๐ ๐ข๐…๐ž๐ฌ๐ญ '๐Ÿ๐Ÿ’ | ๐๐’๐€_๐ƒ๐“๐”
๐‡๐š๐ฉ๐ฉ๐ฒ ๐๐ž๐ฐ ๐˜๐ž๐š๐ซ! | 20240:31๐‡๐š๐ฉ๐ฉ๐ฒ ๐๐ž๐ฐ ๐˜๐ž๐š๐ซ! | 2024
๐‡๐š๐ฉ๐ฉ๐ฒ ๐๐ž๐ฐ ๐˜๐ž๐š๐ซ! | 2024
ะŸะตั€ะตะณะปัะดั–ะฒ 2810 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ
๐‡๐š๐ฉ๐ฉ๐ฒ ๐๐ž๐ฐ ๐˜๐ž๐š๐ซ! | 2024

ะšะžะœะ•ะะขะะ ะ†

  • @singyestudio608
    @singyestudio608 8 ะณะพะดะธะฝ ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 8 ะณะพะดะธะฝ ั‚ะพะผัƒ

    Riad to 450 subs!

  • @singyestudio608
    @singyestudio608 ะ”ะตะฝัŒ ั‚ะพะผัƒ

    Road t0 450 subs!

  • @singyestudio608
    @singyestudio608 8 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road t0 450 subs!

  • @singyestudio608
    @singyestudio608 10 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 15 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road to 450 subs!

  • @KeyserTheRedBeard
    @KeyserTheRedBeard 21 ะดะตะฝัŒ ั‚ะพะผัƒ

    Great video, ๐’๐ˆ๐๐†๐˜๐„ ๐’๐ญ๐ฎ๐๐ข๐จ. Looking forward to your next upload! I smashed that thumbs up button on your content. Keep up the amazing work! Your breakdown of the quotient rule was very clear. How do you think this rule applies in more complex functions, especially when combined with implicit differentiation?

    • @singyestudio608
      @singyestudio608 20 ะดะฝั–ะฒ ั‚ะพะผัƒ

      Thanks for stopping by. The quotient rule still works for the implicit differentiation but one thing to take care about is the chain rule. We shouldn't forget it. For example if we have (2x/y) =3; (simple form), then if we want to find dyldx: 1. We can do implicit differentiation using quotient rule as: 1/y^2* {y2(1) - 2xdy/dx}=0 xdy/dx=y dy/dx=y/x. Just we shouldn't forget the chain rule even in implicit differentiation. 2. Other way: 2x=3y 2=3dy/dx dy/dx=2/3. Though (1) and (2) may look different, they are indeed equal and consistent. In (1), if you substitute x=3y/2 from the original function, it will yield in (1) as: dy/dx=y*{2/3y}=2/3 which corresponds to (2).

  • @singyestudio608
    @singyestudio608 22 ะดะฝั– ั‚ะพะผัƒ

    Support!

  • @singyestudio608
    @singyestudio608 23 ะดะฝั– ั‚ะพะผัƒ

    Support ๐ŸŽ‰.

  • @singyestudio608
    @singyestudio608 23 ะดะฝั– ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 23 ะดะฝั– ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 24 ะดะฝั– ั‚ะพะผัƒ

    Support!

  • @singyestudio608
    @singyestudio608 25 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 25 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Subscribe!

  • @TsheringDeki-ir8yp
    @TsheringDeki-ir8yp 26 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Wow..kaya baat hai..๐ŸŒŸ๐Ÿ‘Œ๐Ÿ‘Œ

    • @singyestudio608
      @singyestudio608 25 ะดะฝั–ะฒ ั‚ะพะผัƒ

      Thanks for watching la. Keep supporting la.

  • @singyestudio608
    @singyestudio608 26 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road to 450 subs!

  • @IconicMamba
    @IconicMamba 27 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Ata how about creating a playlist for 12 maths

    • @singyestudio608
      @singyestudio608 27 ะดะฝั–ะฒ ั‚ะพะผัƒ

      I am discussing syllabus with one of my teachers. I will make la.

  • @singyestudio608
    @singyestudio608 27 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Road to 450 subs!

  • @singyestudio608
    @singyestudio608 28 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Support !

  • @singyestudio608
    @singyestudio608 28 ะดะฝั–ะฒ ั‚ะพะผัƒ

    Support ๐ŸŽ‰!

  • @thinleyjamtsho9687
    @thinleyjamtsho9687 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Versatile person .... Really appreciate your talent boss

    • @singyestudio608
      @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

      Thank you la. Keep supporting la. Share to your friends to make this channel more visible la. Especially aspiring class 11 and 12 children la.

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    400 subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    400 subs?๐Ÿ˜Š

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!

  • @SonamUden-tu9xo
    @SonamUden-tu9xo ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Mister tshering Dendup ๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰๐ŸŽ‰

    • @singyestudio608
      @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

      Yup! He is KETA!

    • @SonamUden-tu9xo
      @SonamUden-tu9xo ะœั–ััั†ัŒ ั‚ะพะผัƒ

      @@singyestudio608 my keta lol๐Ÿ˜†โœจ๏ธ

    • @singyestudio608
      @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

      @@SonamUden-tu9xo oh I see. Good luck

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    DTU

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    400 subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!

    • @mu_el_naught
      @mu_el_naught 21 ะดะตะฝัŒ ั‚ะพะผัƒ

      Congrats on hitting your goal โ€ผ๏ธโ€ผ๏ธ

    • @singyestudio608
      @singyestudio608 20 ะดะฝั–ะฒ ั‚ะพะผัƒ

      @mu_el_naught sure yah. It is only possible due to support from you all. I am always fascinated by proofs in math. Instead of Just memorizing some formulas that your math teacher writes on the board needed to solve some questions on particular topic makes math boring. Although simple mistakes are inevitable but reducible, I enjoy math only when I understand why something equals to sth. Thanks for watching. Keep supporting same.

    • @mu_el_naught
      @mu_el_naught 20 ะดะฝั–ะฒ ั‚ะพะผัƒ

      @@singyestudio608 Same here! I always enjoy seeing the different approaches people have to math problems. Keep it up!

    • @singyestudio608
      @singyestudio608 20 ะดะฝั–ะฒ ั‚ะพะผัƒ

      @@mu_el_naught sure!

  • @FatihouSourouri
    @FatihouSourouri ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Keep going my brother ๐ŸŽ‰๐ŸŽ‰!! You bring more diversity in this channel: physic, science, discover, culture ........

    • @singyestudio608
      @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

      Thank you so much for always supporting!

  • @sangayyouden5458
    @sangayyouden5458 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    ๐Ÿฅฐ๐Ÿฅฐ๐Ÿฅฐ

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!๐ŸŽ‰

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 Subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    Road to 400 subs!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    ๐Ÿ†๐Ÿ…พ๐Ÿ…ฐ๐Ÿ…ณ ๐Ÿ†ƒ๐Ÿ…พ 400 ๐Ÿ†‚๐Ÿ†„๐Ÿ…ฑ๐Ÿ†‚๐Ÿ…ฒ๐Ÿ†๐Ÿ…ธ๐Ÿ…ฑ๐Ÿ…ด๐Ÿ†๐Ÿ†‚!!!

  • @singyestudio608
    @singyestudio608 ะœั–ััั†ัŒ ั‚ะพะผัƒ

    ๐Ÿ†๐Ÿ…พ๐Ÿ…ฐ๐Ÿ…ณ ๐Ÿ†ƒ๐Ÿ…พ 400 ๐Ÿ†‚๐Ÿ†„๐Ÿ…ฑ๐Ÿ†‚๐Ÿ…ฒ๐Ÿ†๐Ÿ…ธ๐Ÿ…ฑ๐Ÿ…ด๐Ÿ†๐Ÿ†‚!!!

  • @singyestudio608
    @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

    ๐Ÿ†๐Ÿ…พ๐Ÿ…ฐ๐Ÿ…ณ ๐Ÿ†ƒ๐Ÿ…พ 400 ๐Ÿ†‚๐Ÿ†„๐Ÿ…ฑ๐Ÿ†‚๐Ÿ…ฒ๐Ÿ†๐Ÿ…ธ๐Ÿ…ฑ๐Ÿ…ด๐Ÿ†๐Ÿ†‚!!! P.S: Sorry for the spelling mistake for "Kruger."

  • @singyestudio608
    @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

    ๐Ÿ†๐Ÿ…พ๐Ÿ…ฐ๐Ÿ…ณ ๐Ÿ†ƒ๐Ÿ…พ 400 ๐Ÿ†‚๐Ÿ†„๐Ÿ…ฑ๐Ÿ†‚๐Ÿ…ฒ๐Ÿ†๐Ÿ…ธ๐Ÿ…ฑ๐Ÿ…ด๐Ÿ†๐Ÿ†‚!!! Request: Sorry for the annoying pencil sound. I will try to be more careful next time.

  • @Rwangmodorjee
    @Rwangmodorjee 2 ะผั–ััั†ั– ั‚ะพะผัƒ

    Nice one sangay youdenโค

    • @singyestudio608
      @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

      She really nailed it.

  • @Kinzang-gq7lm
    @Kinzang-gq7lm 2 ะผั–ััั†ั– ั‚ะพะผัƒ

    Wowโคโค

    • @singyestudio608
      @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

      Thanks!

  • @sangayyouden5458
    @sangayyouden5458 2 ะผั–ััั†ั– ั‚ะพะผัƒ

    Such a beautiful and memorable farewell ๐ŸŽ‰โค๐Ÿ˜Š

    • @singyestudio608
      @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

      Yup, we had. I miss them.

  • @SonamUden-tu9xo
    @SonamUden-tu9xo 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    Tshering oppa๐Ÿ˜‚โคโคโค

    • @singyestudio608
      @singyestudio608 2 ะผั–ััั†ั– ั‚ะพะผัƒ

      Thanks for watching!

  • @NN_Creation3428
    @NN_Creation3428 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    โค

    • @singyestudio608
      @singyestudio608 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

      Thanks for watching!

  • @NN_Creation3428
    @NN_Creation3428 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    โค

    • @singyestudio608
      @singyestudio608 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

      Thanks for watching!

  • @cholmalual4989
    @cholmalual4989 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    Dr. Singye๐ŸŽ‰โค

    • @singyestudio608
      @singyestudio608 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

      Thanks for your support!

  • @singyestudio608
    @singyestudio608 6 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    ๐Ÿ†๐Ÿ…พ๐Ÿ…ฐ๐Ÿ…ณ ๐Ÿ†ƒ๐Ÿ…พ 400 ๐Ÿ†‚๐Ÿ†„๐Ÿ…ฑ๐Ÿ†‚๐Ÿ…ฒ๐Ÿ†๐Ÿ…ธ๐Ÿ…ฑ๐Ÿ…ด๐Ÿ†๐Ÿ†‚!!!

  • @ankitkumaryadav3749
    @ankitkumaryadav3749 7 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    Bhutani Hero @singey bhai โค

    • @singyestudio608
      @singyestudio608 7 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

      Han... ๐Ÿ˜‚๐Ÿ˜‚๐Ÿ˜‚ BHUTANI SALMAN KHAN๐Ÿ˜…

  • @ugyenwangdi1218
    @ugyenwangdi1218 7 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    Shave bro

    • @singyestudio608
      @singyestudio608 7 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

      Lol.

  • @singyestudio608
    @singyestudio608 7 ะผั–ััั†ั–ะฒ ั‚ะพะผัƒ

    Support!