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Power Rule General Form
The Inverse Function Rule can be proved from the Chain Rule as follows. Let y = f(x), x = g(y) be inverse functions whose derivatives exist. Then whence Using the Chain Rule we may write the Power Rule in a general form. POWER RULE Let r be a rational number, and let u depend on x. If u > 0 and du/dx exists, then This is proved by letting y = u^{r} and computing dy/dx by the Chain Rule,


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