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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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