Answer
$$\frac{-9(5 x+\cos 2 x)}{\left(5 x^{2}+\sin 2 x\right)^{5 / 2}}$$
Work Step by Step
Given
$$ y=\frac{1}{(2x^2+\sin 2x)^{3/2}}= (2x^2+\sin 2x)^{-3/2} $$
Then
\begin{align*}
\frac{d y}{d x}&=3\left(-\frac{3}{2}\right)\left(5 x^{2}+\sin 2 x\right)^{-5 / 2}[10 x+(\cos 2 x)(2)]\\
&=\frac{-9(5 x+\cos 2 x)}{\left(5 x^{2}+\sin 2 x\right)^{5 / 2}}
\end{align*}
