OMG! THANK YOU! The textbook doesn’t explain the method #2 how to get to the answers. For anyone who confuses about the part 2 cosh>=1, it is because cosh's range is [1, infinity), that's why you don't need to take the negative root of the function.
3:03 Why should "1+x^2" be used over "x^2+1"? Because the derivative of trig functions often look something like 1/sqrt(1 ± x^n) or something like that? hence the sometimes negative term at the end?
MR. Blackpenredpen, thank you for an awesome video/lecture on the derivative of hyperbolic Sinh inverse of x. I really like the first way, which is an old fashion way for differentiating the hyperbolic Sinh inverse of x.
Ok, took some time, but the recipe is done 1. First, simplify the second term to 1/x^2 (why is it like that?) 2. Then differentiate and get a value of 1/sqrt(ln(x)) (don't worry about the ln(x) in the value) 3. Now, put the value in the original 4. Next, shuffle stuff around to get all the x'es in the numerator 5. Again. differentiate to eliminate the final ln(x) and get a 1/x in it's place 6. Now finally you obtain a quadratic polynomial! A healthy breakfast to start your day! EDIT 2: Gotta show my work, so here: drive.google.com/file/d/1J0qgN_SfpgZZI0r2BR_h9UQQek4LH34H/view?usp=sharing EDIT: Ok problem! I calculate the answer to be +-8^1/4*iota, but cross checking with wolfram, the answer is 8.08104888432933... . All the engines seem to be taking squares, then LCMs and then getting a monster equation where everything is the numerator and then solving it numerically (hit-and-trial per-se (intelligently tho)) As you can see, I differentiated, so a new approach, and it's 4am so I can't get it cross-checked(but no problems i see ;P ) blackpenredpen , WE NEED YOUR HELP
Sounds quite interesting! But there's one thing i dont get: Whats sinh? I mean I know sine, i know cosine, i know arcus sine, but i never really understood what sinh is for...
@@fiNitEarth Try finding a maths teacher or smartboi and ask them to explain it. I usually learn something something new/hard better this way. And yeah, it's high level shit
Why I shouldn't wear this on exams (other than that I've already have these kind of exams many years ago ...)? It's not cheating, I cannot see my back, it's the person's fault behind me because of cheating if (s)he wants to read the derivatives from my back :-P
you have been teaching me math since the 11th grade. i am now in my second year in university. thank you for your immense help
You're doing this in the 2nd year of uni?
If you’re in engineering or take any calculus courses in uni you will need to know this yes :)
@@monicamagdy3595 They teach this in 12th grade here so I was confused why you're learning in uni
Oh my cosh(y)! I love your videos about derivatives of inverse functions!
OMG! THANK YOU! The textbook doesn’t explain the method #2 how to get to the answers. For anyone who confuses about the part 2 cosh>=1, it is because cosh's range is [1, infinity), that's why you don't need to take the negative root of the function.
3:03 Why should "1+x^2" be used over "x^2+1"? Because the derivative of trig functions often look something like 1/sqrt(1 ± x^n) or something like that? hence the sometimes negative term at the end?
So happy to see you have a patreon page!
Thank you and I just saw you've just become a patron. Thank you!
2nd method is more conceptual and understandable. THANK you brother
Thanks sir,
For making all questions solving with two method
I am in first year in university and it helped me a lot. thank you for explaining clearly!
So happy to see you finally got a patreon page and people are supporting you!
You’re a saviour, mathematically and mentally😍
already bought it! little fan from hong kong
#YAY
MR. Blackpenredpen, thank you for an awesome video/lecture on the derivative of hyperbolic Sinh inverse of x. I really like the first way, which is an old fashion way for differentiating the hyperbolic Sinh inverse of x.
This was helpful I at least for the first time in class I got it right
Teacher, how to solve:
1/sqrt(ln x) + 1/sqrt((x^4)) = 1/sqrt(2)?
Well, 1/sqrt(x^4) is x^2, so that's something. And after that you can square both sides maybe?
@@nathansauveur6704 i can not solve. 😓
Ok, took some time, but the recipe is done
1. First, simplify the second term to 1/x^2 (why is it like that?)
2. Then differentiate and get a value of 1/sqrt(ln(x)) (don't worry about the ln(x) in the value)
3. Now, put the value in the original
4. Next, shuffle stuff around to get all the x'es in the numerator
5. Again. differentiate to eliminate the final ln(x) and get a 1/x in it's place
6. Now finally you obtain a quadratic polynomial! A healthy breakfast to start your day!
EDIT 2:
Gotta show my work, so here:
drive.google.com/file/d/1J0qgN_SfpgZZI0r2BR_h9UQQek4LH34H/view?usp=sharing
EDIT:
Ok problem!
I calculate the answer to be +-8^1/4*iota, but cross checking with wolfram, the answer is 8.08104888432933... .
All the engines seem to be taking squares, then LCMs and then getting a monster equation where everything is the numerator and then solving it numerically (hit-and-trial per-se (intelligently tho))
As you can see, I differentiated, so a new approach, and it's 4am so I can't get it cross-checked(but no problems i see ;P )
blackpenredpen , WE NEED YOUR HELP
@@VaradMahashabde Great! But why do you differentiate? Is that even a valid move?
@@VaradMahashabde give me your email? It is easier to exchange these ideas.
This is awesome,it really helps me a lot.
Sounds quite interesting! But there's one thing i dont get: Whats sinh? I mean I know sine, i know cosine, i know arcus sine, but i never really understood what sinh is for...
Thought it was something about weird non eucludian geometry. But you should just google it if you want to learn more, tbh
@@nathansauveur6704 well, it's high level shit and real hard to grasp for me, tbh
@@fiNitEarth Try finding a maths teacher or smartboi and ask them to explain it. I usually learn something something new/hard better this way.
And yeah, it's high level shit
@@nathansauveur6704 thought there could be some smartbois in this comment section :PP
arcus sine?
This was very helpful thanks soo much
Planning on the "two ways" series?
I have been doing that! : )
@@blackpenredpen yeah as an obs. from the two vids
need more different math shirts. already bought the shirt your wearing.
arequina thank you for supporting my channel. More shirts are on the way. : )
@blackpenredpen
Why don‘t you help us out in the discussion about „rad“ in the related rates - triangle - video?
Thank you!
Man, I love you!
I wish I could like this video more than once
Thank you so much 👍
Explain the pronunciation of the hyperbolic functions. They seem to have changed
Hmmm, in that case, I would just say hyperbolic sine, cosine, etc.
Could this be solved using a complex number identity such as Sinh(x) = -iSin(ix) blackpenredpen?
Derivative of sinc(x)
I've ordered a shirt #YAY
The 3rd way:
d/dx(sinh^-1(x))
=d/dx(-i×sin^-1(ix))
=-i×1/√(1-(ix)²)×i
=1/√(1+x²)
Can someone explain why does cosh(y) have to be greater than one ?
First way is easier, but i want to be able to do it both ways to master your class.
Great video, could you make one about the shape of the function f(x)=tan(n*arcos(x))?
second way better thank u
Thank you sir.
That doaraemon music 😅
So good
Use derivative of inverse function
cosh-er maths!!!!!!
#yay!! First. See u rockin that calc t-shirt
thank you x
Implicit differentation
Why I shouldn't wear this on exams (other than that I've already have these kind of exams many years ago ...)? It's not cheating, I cannot see my back, it's the person's fault behind me because of cheating if (s)he wants to read the derivatives from my back :-P
make more of this please
s sdd I have them already. Check my playlists. : )
Both yah :)
pleas I need your help in some question how can I send it for you? Email or face book?
🤩😍😍😋🙂🙂💕💕💕💕💕
can you explain green's theorem? hehe
second way
blackpenredpenbluepen