Answer
$\frac{dy}{dx}=3{(3+\cos^{3}{3x})^{\frac{-4}{3}}}(\cos^{2}{3x}\sin{3x})$
Work Step by Step
$y={(3+\cos^{3}{3x})^{\frac{-1}{3}}}$
on differentiating both sides:
$\frac{dy}{dx}=\frac{d({(3+\cos^{3}{3x})^{\frac{-1}{3}}})}{dx}$
$\frac{dy}{dx}=\frac{-1}{3}{(3+\cos^{3}{3x})^{\frac{-4}{3}}}\frac{d{(3+\cos^{3}{3x})}}{dx}$
$\frac{dy}{dx}=\frac{-1}{3}{(3+\cos^{3}{3x})^{\frac{-4}{3}}}(-9\cos^{2}{3x}\sin{3x})$
$\frac{dy}{dx}=3{(3+\cos^{3}{3x})^{\frac{-4}{3}}}(\cos^{2}{3x}\sin{3x})$
