Let me show you something similar. Perhaps apply it to yours.
Let's show that $\displaystyle \frac{d}{dx}\int_{a}^{g(x)}f(t)dt=f(g(x))g'(x)$
Let u=g(x), then
$\displaystyle \frac{d}{dx}\int_{a}^{g(x)}f(t)dt$
$\displaystyle =\frac{d}{dx}\int_{a}^{u}f(t)dt$
$\displaystyle =\frac{d}{du}\left[\int_{a}^{u}f(t)dt\right]\frac{du}{dx}$
$\displaystyle =f(u)g'(x)=f(g(x))g'(x)$