Math Help - Trouble understanding f of... with derivatives and inverses

1. 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.

2. 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 $f\left(f^{-1}(x)\right)=x\overbrace{\implies}^{\text{chain rule}}f'\left(f^{-1}(x)\right)\cdot\left(f^{-1}(x)\right)'=1$. You can also write this $\left(f^{-1}(x)\right)'=\frac{1}{f'\left(f^{-1}(x)\right)}$