# 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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