Answer
$e^w(5w^2+13w+4)$
Work Step by Step
We are trying to find $\frac{d}{dw}e^w(5w^2+3w+1)$.
Use the Product Rule, $\frac{d}{dw}u(w)v(w)=u'(w)v(w)+u(w)v'(w)$.
In this case, $u(w)=e^w$, so $u'(w)=e^w$. Also, $v(w)=5w^2+3w+1$, so $v'(w)=10w+3$.
Plugging these in, we get:
$\frac{d}{dw}e^w(5w^2+3w+1)$
$=e^w(5w^2+3w+1)+e^w(10w+3)$
$=e^w(5w^2+13w+4)$
