@@ColesWorldofMathematics Still helping people many years later. Thanks so much for the tips and memory helpers. I'm 47 and going back to school and even though I've done tons of math and physics, my memory just isn't what it used to be. These helped a lot along with your other videos.
A trick for memorising the sin, cos integral and derivative is to do: S -C C -S going clockwise from sine gives you the derivative going anti-clockwise gives you the integral. My teacher taught me this and before that, I used to think of its as a shift of the function's graph by 90. So sin(x+90) = cos etc and for each derivative, you add 90 degrees more, so f' '(x) = sin(x+180) which is just -sine for integrals, you do (x-90)
If there is one thing I miss about high school the most was how professors offered memorizing devices like these to students. Remembering sin and cos was relatively easy for me but the other 4 were a pain. This made it so much easier, thank you!!!
At first I was like "oh my gawwwwd, I have to remember all this???" but then I tried it and it turns out I can remember the chart so I'm good. haha. Thanks :P
THANK YOU SO MUCH FOR THESE TIPS! I don't even remember how I ended up here, but I'm so glad I did! As a math/physics tutor (and student, for that matter) I'm ALWAYS struggling to remember all of these seemingly basic derivatives. Every semester I have to refamiliarize myself with each one of these, and this video organizes all of that information so helpfully. I'll be writing down all these notes and using them regularly for my students... can't wait to get to the integral version of this!
You're welcome. When you get to Trig Integrals, you'll have a lot to memorize with those too. Be sure to check out this video for Trig Integrals: ua-cam.com/video/99WvTx29jt0/v-deo.html It uses the same chart!
I really love math but I could never fully enjoy trig. units because the straight up memorization was always so difficult. This helps a TON. Thank you.
THANK YOU SOOOOO MUCH......Most lecturers I watched for these went really fast with these derivatives and would jump over to solving problems. This has helped me sooo much........THANK YOUUUUUUUUUUUUUUUUUUU
The way I remember the anti-derivatives and derivatives of sin or cos is through a level system. If you imagine integration as going up a level and differentiation as going down a level then you just need to remember this: -c s c -s where for derivatives -cosx derives to sinx, sinx derives to cosx, cosx derives to -sinx and then it loops to -sinx derives to -cosx and vice versa for integrals. This is what I was taught by my maths teacher and it helped me out a lot, it's second nature now. When drawing the four letters I say in my head "C, S, C, S - Negatives at the ends"
I don’t understand the use of U’ yet, I have only learned up to the quotient rule and we haven’t covered the chain rule yet, if you’re only taking the first derivative of a trigonometric function do we need the U’ in our equation?
As long as the trig function uses a single "x" variable, you do not need chain rule (u'). In other words, as long as the trig function is not a composite function, you do not need chain rule (u').
We went over it, my teacher taught us to take chain derivatives by reading problems as two parts inside and out, our test on everything derivatives is tmrw and I’m gonna fail it 🤷♂️
this is absolutely phenomenal! god, bless ur dear soul for the amazing video. great quality, very quick, simple, right to the point and very well explained!
THAT"S F* GENIUS !!!!!!!!!! Lady you are the best!!!! OMGsh i was sufferring to memorize those derivatives and hiperbolic derivatives ,but now .. no more !!!! THANK YOU!!!!!!
I must inform you that all six equations written are not true. On the left side of each equation has the Leibniz derivative notation with respect to x. Then on the right of the derivative notation is a trigonometric function with u as its independent variable. Assuming x ≠ u, which was not stated, all six equations are simply wrong (they should all equal zero). You needed to keep both variables the same. The overall idea of this memorization tool for trigonometric derivatives is superb. Though most people glide across this small detail, if shown to a meticulous person it will not go without mentioning. Thank you for sharing this trick and allowing many people to learn from this video.
In the top right hand corner, it states that "u" is in terms of "x", meaning that the "u" in the formula represents a function written in terms of "x". This is common notation found in many Larson Calculus Books (written by Ron Larson).
For the longest time I've had to go back and memorize these before every test. You've saved me so much time I can't thank you enough.
So glad it has helped you! Thanks for watching!
Literally same
@@ColesWorldofMathematics Still helping people many years later. Thanks so much for the tips and memory helpers. I'm 47 and going back to school and even though I've done tons of math and physics, my memory just isn't what it used to be. These helped a lot along with your other videos.
You just turned what was about to be an hour-and-a-half long study session into a five minute video and probably a lifelong understanding. Thanks dude
Glad it was helpful!
A trick for memorising the sin, cos integral and derivative is to do:
S
-C C
-S
going clockwise from sine gives you the derivative
going anti-clockwise gives you the integral.
My teacher taught me this and before that, I used to think of its as a shift of the function's graph by 90.
So sin(x+90) = cos etc
and for each derivative, you add 90 degrees more, so f' '(x) = sin(x+180) which is just -sine
for integrals, you do (x-90)
thanks so much
@@ian.jeonkook I googled it and it shows as -sinx
@@Hyvexx ahh sorry my bad. i used chat gpt earlier for this .this goddamn app gives me shit tons of wrong ans. ty tho
Pretty neat too!! Thanks for sharing!
Thanks a ton
the simplicity of your explanation makes me wish I had seen this when I was tutoring in the university math lab.
Thanks for the compliment.
If there is one thing I miss about high school the most was how professors offered memorizing devices like these to students. Remembering sin and cos was relatively easy for me but the other 4 were a pain. This made it so much easier, thank you!!!
You're welcome. Your statement is very true. Memorization techniques are always very helpful, and generally not shared or taught at the college level.
At first I was like "oh my gawwwwd, I have to remember all this???" but then I tried it and it turns out I can remember the chart so I'm good. haha. Thanks :P
You're welcome! Glad it was helpful! Thanks for watching.
THANK YOU SO MUCH FOR THESE TIPS! I don't even remember how I ended up here, but I'm so glad I did! As a math/physics tutor (and student, for that matter) I'm ALWAYS struggling to remember all of these seemingly basic derivatives. Every semester I have to refamiliarize myself with each one of these, and this video organizes all of that information so helpfully. I'll be writing down all these notes and using them regularly for my students... can't wait to get to the integral version of this!
You're welcome! Glad it was very helpful! Please share my channel with the students you tutor.
integral version is embedded. group up the first two from the left (or last two from the right) and you get the integral
This is amazing, it makes me wonder why they don’t teach this in Calc and instead just tell us to memorize, thank you so much!
Glad it was helpful!
I think you've just saved my semester! I was going crazy trying to memorize everything - I wish my professors had taught me this method! Thank you!
You're welcome. When you get to Trig Integrals, you'll have a lot to memorize with those too. Be sure to check out this video for Trig Integrals: ua-cam.com/video/99WvTx29jt0/v-deo.html It uses the same chart!
YOU SAVED MY LIFE!!! THANK YOU SO FRICKING MUCH!!!!!!
You’re welcome! Glad the video was helpful!
Very useful and to-the-point video; thank you, Ms. Cole!
You're welcome!
I really love math but I could never fully enjoy trig. units because the straight up memorization was always so difficult. This helps a TON. Thank you.
WHOA this is so amazing!! Thank you so much you just saved my brain cells
So glad the video was helpful for you! Thanks for watching. 💜
Thanks man! You've reduced my pressure by a lot!!
Great to hear! Thanks for watching.
THANK YOU SOOOOO MUCH......Most lecturers I watched for these went really fast with these derivatives and would jump over to solving problems. This has helped me sooo much........THANK YOUUUUUUUUUUUUUUUUUUU
So glad you found the video helpful! 😊
Found this absolute life saver right before a midterm. Thank you so so much!!!
Glad it helped! Hope you did well on your midterm.
I'm in cal 3 and I've never seen this before. Thank you!
You're welcome! Hope it was helpful! Thanks for watching.
You are so kind for showing us this trick! Thank you so much!!!!! This is going to help me alot
You're welcome! Glad it was helpful!
You saved my time, Thanks!
You are welcome! Glad it helped!
So easy to memorize now. Thank you so much!
You are welcome. Glad it helped!
man... so much time was saved from me trying to memorize these functions. God bless you.
Glad the trick was helpful for you!
Thanks alot
I've been having difficulty memorizing this, you just made it a lot easier.
Glad to hear that!
This helped so much! I would have never thought of this trick.
Thanks! Glad you found the video! Thanks for watching!
I got a 100 on that exam, very useful
this is soo helpful! thank you!
+Maria Ruiz You're welcome! Glad it was helpful!
That was a lifesaver. Thanks!
Glad it helped! Thanks for watching.
Thank you so much sir Cole!
Very welcome!
you're a genius
Thanks, but this original idea is available all over the internet, I did not come up with it, I just made a video to easily explain it. 😁
This video has saved so many grades. Thank you!
You’re welcome! Thanks for watching!
thank you soooo much I went into youtube hoping I would find a trick but I didn't expect to find one this good
Glad it was helpful!
This was a wonderfully simple and effective trick. Thank you so much!
Glad you liked it! Thanks for watching & commenting!
The way I remember the anti-derivatives and derivatives of sin or cos is through a level system. If you imagine integration as going up a level and differentiation as going down a level then you just need to remember this:
-c
s
c
-s
where for derivatives -cosx derives to sinx, sinx derives to cosx, cosx derives to -sinx and then it loops to -sinx derives to -cosx and vice versa for integrals. This is what I was taught by my maths teacher and it helped me out a lot, it's second nature now.
When drawing the four letters I say in my head "C, S, C, S - Negatives at the ends"
Thanks! I have had one other person tell me the same trick. It's a good way to remember sin and cos. Thanks for the trick and thanks for watching.
This is a very creative and easy way to remember these trig derivatives!
Thank you so much!
This is a GREAT memory tool. Thank you so much!
You're very welcome! I'm glad you found it helpful! Thanks for watching and posting.
Thank you so much! I was about to memorize this and the trig integrals and you saved me so much time! Easy to follow and understand!!(:
Glad it was helpful.
thankyou so much for this and the one on integrals... saved my time
You're welcome! Glad it helped!
this was like incredibly life changing
Thanks so much! Glad it helped you out!
Thank you Cole. This is an awesome teaching. I have both charts saved for memorization and clicked like and pressed subscribe.
Awesome, thank you!
I don’t understand the use of U’ yet, I have only learned up to the quotient rule and we haven’t covered the chain rule yet, if you’re only taking the first derivative of a trigonometric function do we need the U’ in our equation?
As long as the trig function uses a single "x" variable, you do not need chain rule (u'). In other words, as long as the trig function is not a composite function, you do not need chain rule (u').
We went over it, my teacher taught us to take chain derivatives by reading problems as two parts inside and out, our test on everything derivatives is tmrw and I’m gonna fail it 🤷♂️
THIS IS SOOOOO HELPFUL TYSM ILY
No problem!! 👍🏻
This is so genius! Thanks Bro!
Glad you like it!
AMAZING!!!! THANK YOU !!!!
You're Welcome! Hope it helped!
YOU ARE A LIFE SAVER!
😀 Thanks for watching.
Excellent Approach
Thanks!
this just changed my life
So glad it helped! Thanks for watching.
thank you very much for your help!
+Gabriel Veloz You're welcome!
Wow, thank you for explaining the relationship in such a simple manner!
You’re welcome!
Loved this video, thanks ms cole :-)
Glad you enjoyed it! Thanks for watching.
Very helpful and an easy chart to remember! Thanks.
You are welcome! Thanks for watching!
thank you so much! basically saved me from excruciating hours of memorizing :)
You're welcome! Glad it helped!
This is amazing. Thank you!
Glad you like it! Thanks for watching & commenting.
this is awesome yet so simple, thanks!
You're welcome!
very underrated video, and it is saving my life the night before a test lol
Great to hear that! Thanks for watching!
This is so helpful, thank you!
Glad it was helpful! Thanks for watching.
You are Amazing! Thank you!!
You're so welcome!
You ma'am are the 🐐
this is absolutely phenomenal! god, bless ur dear soul for the amazing video. great quality, very quick, simple, right to the point and very well explained!
Thanks! Glad you enjoyed the video! Thanks for watching.
I had my doubts when I clicked on this video, but this was immensely helpful.
Glad you found it helpful! Thanks for watching!
Sir. You. Are. A. Legend!
Thanks! 👍🏻😊
This is so helpful
Thank you very very much for this easy memorization trick!!!
Most welcome!
wow, what a great help! thank you very much.
You are welcome! Thanks for watching. Please share with your friends.
Wow this is so much better than listening to the trig derivative song 1000 times vs using 6 words to remember the 6 trig derivatives!
Glad the video was helpful! Thanks for watching & commenting!
Holy crap where were you when I took this course a few years ago. I just needed a quick refresher for my current class and now I'm set lol
Glad the video was helpful!
@@ColesWorldofMathematics me too lol
YOU ARE A LIFE SAVER.
5 HOURS TILL MY CALCULUS FINAL EXAM
Good Luck!!!! 👍🏻
OMG I am so glad I searched this up...
Me too. Thanks for watching.
OMG I just wrote a calculus test that was sooo tricky yesterday that I did not finish... but with this, I swear I am ready to pass
👍🏻
Wonderful memorizing tricks!!!!
Thanks!
Can you use this for integrals too? I've notived the integral of cosecx is -ln(cosec + cot) and it works for a few others
Here is a video for memorizing Trig Integrals: ua-cam.com/video/99WvTx29jt0/v-deo.htmlsi=JgGIbAXUjIXuEjCe
It uses the same mnemonic device.
@@ColesWorldofMathematics this is golden thank you
THAT"S F* GENIUS !!!!!!!!!! Lady you are the best!!!! OMGsh i was sufferring to memorize those derivatives and hiperbolic derivatives ,but now .. no more !!!! THANK YOU!!!!!!
You’re welcome! My goal is always to make things easier to memorize!
This is amazing thank you so much!
You're welcome! Thanks for watching.
This is so helpful I couldn't memorize these until now
Glad it helped you out!
Helped a lot !!! Thank u
You’re welcome! Thanks for watching!
This is so helpful. Thanks bro
No problem!
Thank you! I forgot all my calculus and need to take the math GRE and this channel is a godsend!w
Glad it will be helpful!
super helpful and simple thank you!!!
That’s awesome! Thanks for watching!
Helped a lot!! Thanks you so much 😍
Really glad the trick was helpful! Thanks for watching.
i am not even kidding you are saving my life right now
Great video! Is there any quick way to memorize the derivatives of aall inverse trig functions like arccos?
Yep - ua-cam.com/video/NI9Avfc9K2M/v-deo.html
Wow it's amazing . Please also share a trick to remember derivative of inverse trigonometric functions.
ua-cam.com/video/NI9Avfc9K2M/v-deo.html
itss an awesome method. thanx for this
You are welcome. Thank you for watching!
Thank you for sharing this.
My pleasure! Thanks for watching & commenting!
I always remember that if it starts with "C", there will be a negative sign in it
Several of my students have used that as a mnemonic. 👍🏻
You're a life savour thankyou
You're welcome! Thanks for watching.
So helpful! Thank you I have my calc exam tomorrow
Hope it went well for you!
You are amazing!!!!!!! thank you!!!!!
You're so welcome!
Thank you so much. I always mixed derivatives of cot and csc
You're welcome!
i love this man
Thanks!
So helpful!
Thanks! Always glad when a video helps someone!
Cole's World of Mathematics ma'am I've been trying to learn these for like ages and this video has saved a life! Lots of love! Thank you!! Xo
absolute lifesaver
Wow! this is very helpful!
Glad it was helpful!
Nice one. Thank you!
You're welcome!
I must inform you that all six equations written are not true. On the left side of each equation has the Leibniz derivative notation with respect to x. Then on the right of the derivative notation is a trigonometric function with u as its independent variable. Assuming x ≠ u, which was not stated, all six equations are simply wrong (they should all equal zero). You needed to keep both variables the same. The overall idea of this memorization tool for trigonometric derivatives is superb. Though most people glide across this small detail, if shown to a meticulous person it will not go without mentioning. Thank you for sharing this trick and allowing many people to learn from this video.
In the top right hand corner, it states that "u" is in terms of "x", meaning that the "u" in the formula represents a function written in terms of "x". This is common notation found in many Larson Calculus Books (written by Ron Larson).
Thank you so very much!!
No worries!
Cole’s world must be a very beautiful one. Thanks for this.
You’re welcome.
So helpful thank you!!!
You’re welcome!
Wow! Thanks man
You bet!
Thank you this saved me hours of flashcards
Least glad when my videos help someone! 👍🏻😃 Thanks for watching!
Life saver, thank youu
Happy to help!
It helped me , thank you so much madam , God bless you.
You’re welcome! Thanks for watching!
Excellent 👌🏻
Thanks!