Induction proof for the nth derivative of x e^{2x}

A function $f$ has the rule $f(x) = x\,e^{2x}$.

Use mathematical induction to prove that $f^{(n)}(x) = \left(2^n x + n\,2^{n-1}\right)e^{2x}$ for $n \in Z^+$, where $f^{(n)}(x)$ represents the $n^{\text{th}}$ derivative of $f(x)$. That is, $f(x)$ has been differentiated $n$ times.