My Math Forum Differentiation

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November 14th, 2016, 05:21 PM   #1
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Differentiation

Anyone??
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 November 15th, 2016, 05:48 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,515 Thanks: 640 The problem is: given two differentiable functions, f and g, with f(x) > 0, show that $\displaystyle e^{g(x)\ln(f(x))}$ is differentiable. Looks to me that the best way to do that is to differentiate it! The derivative is, of course, $\displaystyle e^{g(x)\ln(f(x))}$ times the derivative of g(x)ln(f(x)). And that is, by the product rule and chain rule, $\displaystyle g'(x)\ln(f(x))+ \frac{g(x)f'(x)}{f(x)}$. Since f and g are differentiable, f' and g' exist and since f(x) > 0, f is never 0 so that clearly exists. Last edited by skipjack; November 15th, 2016 at 07:02 AM.

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