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

  1. #1
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    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.
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Cakecake View Post
    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)}
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