Derivative of inverse sine | Taking derivatives | Differential Calculus | Khan Academy

Differential calculus on Khan Academy: Limit introduction, squeeze theorem, and epsilon-delta definition of limits.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

For free. For everyone. Forever. #YouCanLearnAnything

Subscribe to KhanAcademy’s Differential Calculus channel:

[varun]

When I'm done with school, I'm gonna start math from the beginning (not really the beginning, but from where I'm comfortable) just because you make so much sense of it all. I love the way you teach.

Update: I have learnt a great deal. I've recently completed ODEs, particularly wronskian theorem and uniqueness theorem. Ive gotten over my fear of trigonometry and statistics. It's been great ever since i started working in insurance, especially since I now have some money to play the stock market. Keep at it, guys. KA doesn't have everything, but it will, at the very least, position you to better understand published texts without tuition.

[cmjelsdal]

There's a general formula for finding the derivative of a function from it's inverse function. You start by defining g(x)=f-1(x) (the inverse of f(x)). You can then write that f(g(x))=x since that is the very definition of an inverse function. If we then differentiate both sides with respect to x, we get d/dx[f(g(x))]=d/dx[x]. On the left we use the chain rule and get f'(g(x))*d/dx[g(x)], and on the right we get 1. Solve for d/dx[g(x)] and you get d/dx[g(x)]=1/f'(g(x)). You can even find the integral of a function from its inverse function but that i'm not going to tell. If someone finds/wants the answer please write me a comment because i would love to know :) 

Hint: It involves f(g(x))*g'(x)

[Mistiigolden]

I am currently studying for my AP Calculus AB midterms and this helped tremendously. I have been scared of inverse trig for some time now, and your videos are helping me work to overcome this fear. Thank you.

[LyndenBlyndenHD]

My teacher tried explaining this, differentiating arctan and improper integrals in 3 hours and I got nowhere, I’ve watched 15 mins worth of your videos and I get it, thank you so much

[thegiraffegoesmoo]

Amazing method to find the derviative of inverses. My teacher was trying to explain it with all these whacky formulas and stuff but it just didn't hit. This easily cleared up everything and finally makes so much sense!

[Arch.A]

Your voice calms me,
tells me that every thing is ok, you gonna do good in tomorrow’s exam and your whole math journey in your life 🙏🏻♥️

[amirafiqamirul]

Thank You shoo much..now i understand what is inverse trigo derrivative..my lect always said to us to memorizing this thing..but...meh..what is the function if we mem. without knowing where it come from..thanks..feeling happy rite nw..

[daedra]

The Drum roll is inherent for Sal's work. He makes it's all so clear and enlightening :D

[shyamchandran]

Thank u so much Khan academy. I fell in love with maths

[swathynatarajan]

This was pretty straightforward (even more so if you take the graph of the sine function; the sine is an odd function so the sign doesn't change, and for every change of y, the change of x is the period of the cosine wave. Now substitute to get the derivative wrt sine and there we have the answer.

[Pendragon]

Thank you so much for this! I don't know why but this makes everything so much simpler...

[IsaacSechslingloff]

ALTERNATIVE METHOD. Using the derivative of inverse property, I didn't simplify it further but on DESMOS it produces the same graph as this answer. I would imagine with some trig properties it reduces to this answer

[davidFbeckham]

the way my textbook explains this is ABYSMAL! Thank you so much!

[Mrius]

Two months into Calc 1 and I am finally able to take derivatives of inverse trig functions. It takes a lot of hard work. Looking at different problems. Using the Pythagorean identity, sin^2x+cos^2x=1.

[JogilB]

This is just beautiful!! =) the beauty of mathematics!

[BelievinSP]

Oh wow I never knew that.  I've always just know them.  Thanks for the video.

[cmjelsdal]

Thank you Sal for still coming with interesting videos. DFTBA :D

[abdeljalilelhayanimarzoqi]

Thank you so much for the clear explanation

[kusumlata]

Great and clear cut lecture... Love it... ❤️❤️

[blacklightning]

thanks Genghis.... i needed this to understand how the derivative table ended up with this...