Question

find f(x).
f(x)=4xe^x
f(x)=□

Explanation:

Step1: Apply product - rule

The product - rule states that if $y = u\cdot v$, then $y'=u'v + uv'$. Here, $u = 4x$ and $v = e^{x}$.

Step2: Find $u'$ and $v'$

The derivative of $u = 4x$ with respect to $x$ is $u'=4$. The derivative of $v = e^{x}$ with respect to $x$ is $v'=e^{x}$.

Step3: Calculate $f'(x)$

Using the product - rule $f'(x)=u'v + uv'$, we substitute $u = 4x$, $u' = 4$, $v = e^{x}$, and $v' = e^{x}$. So $f'(x)=4e^{x}+4xe^{x}=4e^{x}(1 + x)$.

Answer:

$4e^{x}(1 + x)$