What is the derivative of $x e^{x}$ $xe^x$ ?

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Answer 1 · 2014-12-17T17:45:57

To evaluate this derivative you use the product rule .

When you have a function that is the product of 2 functions $f (x)$ $f(x)$ and $g (x)$ $g(x)$ you can derive it as:

$d/(dx)f(x)g(x)=f'(x)g(x)+f(x)g'(x)$

In your case:

$f(x)=x and f'(x)=1$
$g(x)=e^x and g'(x)=e^x$

Finally deriving the complete function we have:

$d/(dx)xe^x=1e^x+xe^x=e^x(x+1)$

What is the derivative of xe^xxexxe^x?