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I want to find derivative of following function defined in proper domain w.r.t x

$$ e^{3x} \log{2x} $$

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Do you mean $e^{3x}\log (2x$)? If so, you need braces around the $3x$ to make the $x$ come out in the exponent. Or is it $\log_2 (x)$? – Ross Millikan May 16 '11 at 13:19
In any case of the problem, do you know the multiplication and chain rules for derivatives? – Ross Millikan May 16 '11 at 13:21
Please write this in question form, not in request form. – Asaf Karagila May 16 '11 at 15:32

Use the product rule which says that if $f$ and $g$ are differentiable functions then $(f(x)g(x))' = f(x) \cdot g'(x) + g(x) \cdot f'(x)$ and note that the derivative of $e^{ax}= ae^{ax}$ for some $a \neq 0$ and derivative of $\log{x}$ is $\frac{1}{x}$

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@Ross: Typo, forgive me – user9413 May 16 '11 at 15:47
@Ross: I have rectified it. Thanks for pointing out the error. – user9413 May 16 '11 at 15:49

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