The discussion revolves around finding the derivative of an inverse function in the context of calculus. The original poster presents a problem involving a differentiable function and its inverse, utilizing the relationship f(f-1(x)) = x.
The discussion is ongoing, with participants exploring different approaches to the problem. Some guidance has been offered regarding the use of implicit differentiation and the chain rule, but there is no explicit consensus on the correct method or solution yet.
Participants are working under the constraints of homework rules, which may limit the extent of guidance provided. There is an emphasis on understanding the derivation process rather than arriving at a final answer.
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?harrietstowe said: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