Answer
$f'(x)=-3[x+csc(x^{3}+3)]^{-4}\cdot [(1-3x^{2})csc(x^{3}+3)cot(x^{3}+3)$
Work Step by Step
Use chain rule
$f'(x)=-3[x+csc(x^{3}+3)]^{-4}.\frac{d}{dx}[x+csc(x^{3}+3)$
$=-3[x+csc(x^{3}+3)]^{-4}.[1+(-csc(x^{3}+3)cot(x^{3}+3))(3x^{-2})$
$=-3[x+csc(x^{3}+3)]^{-4}.[(1-3x^{2})csc(x^{3}+3)cot(x^{3}+3)$
