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Calculus Inverse function Derivative problem

  • #1

Homework Statement



f is a function with an inverse and it is differentiable. Use f(f-1(x))=x
and come up with the formula for the derivative of f-1

Homework Equations





The Attempt at a Solution


I tried expanding that equation to f'(f-1(x))*f'-1(x) -x
but I tested this and it didn't work.

Thanks
 

Answers and Replies

  • #2
vela
Staff Emeritus
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You started with an equation, and then you ended up without one. Could you describe what you did more carefully?
 
  • #3
52
0

Homework Statement



f is a function with an inverse and it is differentiable. Use f(f-1(x))=x
and come up with the formula for the derivative of f-1

Homework Equations





The Attempt at a Solution


I tried expanding that equation to f'(f-1(x))*f'-1(x) -x
but I tested this and it didn't work.

Thanks
You should just take the derivative of both sides. Use the chain rule on the left hand side.... Where did your equality go, and where did the -x come from?
 
  • #4
612
1
use implicit differentiation
 

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