Answer
$$ f'(x)
=\frac{\sin x-x\cos x+2}{(\sin x+2)^2} .$$
Work Step by Step
Since $ f(x)= \frac{x}{\sin x+2}$, then using the quotient rule, the derivative is giving by
$$ f'(x)=\frac{(\sin x+2)(1)-x(\cos x)}{(\sin x+2)^2} \\
=\frac{\sin x-x\cos x+2}{(\sin x+2)^2} .$$
