How do you derive this equation:
y = sin ^ 3 (cosx^3)
You need to use the chain rule several times:
$\displaystyle y=\sin^3\cos x^3=\left(\sin\cos x^3\right)^3$
$\displaystyle \Rightarrow\frac{dy}{dx}=3\sin^2\cos x^3\cdot\frac d{dx}\left[\sin\cos x^3\right]$
$\displaystyle =3\sin^2\cos x^3\left(\cos\cos x^3\cdot\frac d{dx}\left[\cos x^3\right]\right)$
And so on. Can you continue?