Derivatives of Inverses #15

Question

Suppose  is a one-to-one, differentiable function and its inverse function  is also differentiable. One can show, using implicit differentiation (do it!), that

Find  if  and .

Answer 1

Hi

Find  if  and .

when ------> f^-1(-4 ) = -2

when ------>( f^-1(-4))' = 1/(f'(-2) -----> 7/2

in fact, x at left side is y for x at right side.

on the other word, you need to figure out that A(x₁,y₁) belongs to the function AND B ( y₁,x₁) belongs to the the inverse, so x at left side is y₁ and x at the right side is x₁

_{I hope it is useful,}

_Minoo