What is the derivative of $f(x) = -5 e^{xcos x}$ ?

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What is the derivative of $f(x) = -5 e^{xcos x}$ ?

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Answer 1 · 2015-08-04T16:57:11

I found: $f'(x)=-5e^[xcos(x)]xx[cos(x)-xsin(x)]$

Explanation:

Here I would use the Chain Rule to deal first with $e$ (red) and then with the exponent (blue where you need the Product Rule):
$f'(x)=-5color(red)(e^[xcos(x)])xxcolor(blue)([1*cos(x)-x*sin(x)])$

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What is the derivative of $f(x) = -5 e^{xcos x}$ ?

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What is the derivative of $f(x) = -5 e^{xcos x}$ ?