So I have to function $x^2e^{-x}$. Do I derivative that like $f' g+g' f$ or $f' g'$? I'm not sure because it is derivative over x so if you can help me.
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2product rule: $(fg)'=f'g+g'f$ – voldemort Jan 26 '14 at 19:09
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Note that $e^{-x}$ is a function inside function – k1ber Jan 26 '14 at 19:14
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It is the product rule that you need. So with $f(x) = x^2$ and $g(x) = e^{-x}$, you get the derivative of $f(x)g(x)$ $$f'(x)g(x) + f(x)g'(x). $$
Thomas
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Any time you have multiplication, use the product rule $(fg)' = f'g + fg'.$
Any time you have one function inside another function (composition), use the chain rule.
In this case, you have $x^2$ times $e^{-x}$, so you use the product rule. $f(x) = x^2$, $g(x) = e^{-x}$. Can you manage from here?
