Prove Inverse Function Derivative theorem (1 Viewer)

Pedro123

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Hey Guys,

This is 1A Question 24 c) of the Cambridge Math 2012 3 unit textbook:
If f is a differentiable function for all real x and has an inverse function g, prove that:

Where f'(g(x)) is not 0
 

Trebla

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Same thing but another way to look at it:
dy/dx = 1/(dx/dy)
If y = g(x) and equivalently x = f(y) then
g’(x) = 1/f’(y)
and the result follows
 

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