Formula for Computing a Derivative of an Inverse Function

Let

$f(x)$

be a monotonic function and differentiable at point t. We note:

$f(t)=b$

If

$f'(t)\neq 0$

Then

$f^{-1}(x)$

is differentiable at point b and the following holds:

$(f^{-1})' (b) = \frac{1}{f'(f^{-1}(b))}$

In short, remember this formula:

$(f^{-1})' (x) = \frac{1}{f'(f^{-1}(x))}$

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