How do you differentiate $y=xe^x$ ?

Question

42096 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-23T14:54:34

$frac{"d"}{"d"x}(xe^x) = (1 + x) e^x$

The product rule:

If $u$ and $v$ are differentiable functions of $x$ ,

and $f = u * v$ ,

then $f' = u' * v + u * v'$ ,

where the apostrophe denotes the derivative with respect to $x$ .

In the above question, we can see that $x e^x$ is a product of $x$ and $e^x$ , both which are elementary functions.

Thus

$frac{"d"}{"d"x}(xe^x) = frac{"d"}{"d"x}(x) e^x + x frac{"d"}{"d"x}(e^x)$

$= (1) e^x + x (e^x)$

$= (1 + x) e^x$

How do you differentiate y=xe^xy=xe^x?