Question

find the derivative of the function y = xe^{2x}
select the correct answer below:
○ e^{2x}(2x + 1)
○ e^{2x}+2x
○ e^{2x}+1
○ 2xe^{2x}+2x

Explanation:

Step1: Apply product - rule

$(uv)' = u'v+uv'$, where $u = x$, $v = e^{2x}$.

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

$u'=1$, $v' = 2e^{2x}$ by chain - rule.

Step3: Calculate $y'$

$y'=1\times e^{2x}+x\times2e^{2x}=e^{2x}(2x + 1)$

Answer:

$e^{2x}(2x + 1)$