find f(x). f(x)=13xe^x f(x)=□

Explanation:

Step1: Recall product - rule

The product - rule states that if $y = uv$, where $u$ and $v$ are functions of $x$, then $y^\prime=u^\prime v + uv^\prime$. Here, $u = 13x$ and $v = e^{x}$.

Step2: Find $u^\prime$ and $v^\prime$

The derivative of $u = 13x$ with respect to $x$ is $u^\prime=13$ (since the derivative of $ax$ with $a = 13$ is $a$). The derivative of $v = e^{x}$ with respect to $x$ is $v^\prime=e^{x}$.

Step3: Apply product - rule

$f^\prime(x)=u^\prime v+uv^\prime$. Substituting $u = 13x$, $u^\prime = 13$, $v = e^{x}$, and $v^\prime=e^{x}$ into the product - rule formula, we get $f^\prime(x)=13e^{x}+13xe^{x}=13e^{x}(1 + x)$.

Answer:

$13e^{x}(x + 1)$