# Trouble understanding f of... with derivatives and inverses

• Oct 20th 2008, 12:51 PM
Cakecake
Trouble understanding f of... with derivatives and inverses
Things such as f', f^-1, (f^-1)', etc.

I'd like to know the relation between them and how to get from 1 to another. Most of the times I see that the answer is 1 over a certain number. If this is confusing I'll try to find a sample problem.
• Jan 6th 2009, 06:39 PM
Mathstud28
Quote:

Originally Posted by Cakecake
Things such as f', f^-1, (f^-1)', etc.

I'd like to know the relation between them and how to get from 1 to another. Most of the times I see that the answer is 1 over a certain number. If this is confusing I'll try to find a sample problem.

I think this might be what you are looking for. Consider that $\displaystyle f\left(f^{-1}(x)\right)=x\overbrace{\implies}^{\text{chain rule}}f'\left(f^{-1}(x)\right)\cdot\left(f^{-1}(x)\right)'=1$. You can also write this $\displaystyle \left(f^{-1}(x)\right)'=\frac{1}{f'\left(f^{-1}(x)\right)}$