Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![Suppose \( f \) is a one-to-one differentiable function, and its inverse function \( f^{-1} \) is also differentiable. Use implicit differentiation to show that
\[
(f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))}.
\]](https://content.bartleby.com/qna-images/question/a2582775-6eba-4cab-84a0-ce83b57b223b/9f1cf028-8394-4905-8593-41417825642e/l777va_processed.png)
Transcribed Image Text:Suppose \( f \) is a one-to-one differentiable function, and its inverse function \( f^{-1} \) is also differentiable. Use implicit differentiation to show that
\[
(f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))}.
\]
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