# How do you calculate the derivative of int5(sin(t))^5 dt from [e^x,5]?

$5 \frac{d}{\mathrm{dx}} {\int}_{{e}^{x}}^{5} {\sin}^{5} t \mathrm{dt} = = - 5 {e}^{x} {\sin}^{5} \left({e}^{x}\right)$
$5 \frac{d}{\mathrm{dx}} {\int}_{{e}^{x}}^{5} {\sin}^{5} t \mathrm{dt} = - 5 \frac{d}{\mathrm{dx}} {\int}_{5}^{{e}^{x}} {\sin}^{5} t \mathrm{dt}$
$= - 5 {\sin}^{5} \left({e}^{x}\right) \frac{d}{\mathrm{dx}} \left({e}^{x}\right) = - 5 {e}^{x} {\sin}^{5} \left({e}^{x}\right)$