Proof for derivative of sine inverse trig function

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#InverseFunctions #InverseDerivatives #Calculus
Derivative of Inverse Functions: Inverse function has reciprocal slope at corresponding points.
Prove
(f^(-1) )'(x)=1/(f^' (f^(-1) (x)) )

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A proof this simple and elegant... I don't understand why my math teacher wouldn't spend five and a half minutes to show something like this to my class when I were in college.
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Actually, thinking back to how my class were, perhaps they were right not to waste the time. :)

XregularC_Casual

This is exactly what Einstein meant when he said, "If you can't explain it simply, you don't understand it enough."

marcoskano

You make it easly to understand for me sir. Thx for your sollution for my confution 🙏

jobdaniel

Thank you for a different approach from anything else I’ve seen

HillbillyfromAL

Sir there is a small mistake in the video: while you were saying domain you wrote range of sin

itsmemario

Can you actually prove the inverse trig functions like

Sin(arccos(x)) etc. using derivatives? I don’t know tbh

Algebrainiac

Thank you a lot finally I got one can explain very easy way
I understand finally

zezenyaqatar

Best proof ever.❤❤❤❤❤❤❤❤take respect sir.😊

hasanabdullah-huls

Thank you so much, this proof is so easy to understand

ejosh

why is dy/dx = 1/cos y?

ETA: Oh I get it he isolated dy/dx via transpoing cos y to the other side(via division of both sides by cos y)

lancegabrieltanedo

Can someone explain why the range is between -pi/2 and pi/2?

joshuamwangi

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