Suppose that we have (on some domain) a 1 - 1 function y(x). So we can alternatively write x(y). Consider a point x_0 and let y_0 = y(x_0). Suppose(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{dy}{dx}(x_0) = f(x_0)[/tex]

Is it always true that

[tex]\frac{dx}{dy}(y_0) = \frac{1}{f(x(y_0))}[/tex]

? If not, under what conditions might it be false?

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# Inverting a derivative

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