Product rule with a power function and an exponential

Identify the two factors being multiplied: $u(x) = x^3$ and $v(x) = e^x$. Their derivatives are $u'(x) = 3x^2$ and $v'(x) = e^x$, using the power rule and the fact that $e^x$ is its own derivative.

Apply the product rule $f'(x) = u'(x)v(x) + u(x)v'(x)$ to get $f'(x) = 3x^2 e^x + x^3 e^x$. Factoring out the common term $x^2 e^x$ gives the simplified form $f'(x) = x^2 e^x(3 + x)$.