# Calc2.14

Find the derivative of $f(x)\,$ with respect to $x\,$: $f(x)=\int _{{4}}^{{x^{2}}}\sin(e^{t})\,dt\,$
This problem uses the Second Fundamental Theorem of Calculus but it also uses the Chain Rule. Since the upper limit of the integral is not plain $x\,$, then we must multiply by the derivative of the inside function just as we would in any other chain rule problem.
$f'(x)=\sin(e^{{x^{2}}})(2x)\,$
The $\sin(e^{{x^{2}}})\,$ came from plugging the upper limit $x^{2}\,$ into the inner function, $f(t)\,$ and the $2x\,$ came from multiplying by the derivative of $x^{2}\,$.