Compute $f^{\text{'}\text{'}}(x)$ where $f(x)={\displaystyle \underset{0}{\overset{x}{}}}{e}^{t^2}dt$

$($a$)e^{x^2}$

$($b$)2x{e}^{x^2}$

$($c$)x{e}^{x^2}$

$($d$)e^{2x}$

$($e$)\frac{1}{2}{e}^{x^2}$