# Question #cafe0

$\frac{d}{\mathrm{dx}} \left({\cos}^{3} \left(x\right)\right) = 3 {\cos}^{2} \left(x\right) \cdot \left(- \sin \left(x\right)\right) = - 3 {\cos}^{2} \left(x\right) \sin \left(x\right)$
Use the Chain Rule $\frac{d}{\mathrm{dx}} \left(f \left(g \left(x\right)\right)\right) = f ' \left(g \left(x\right)\right) \cdot g ' \left(x\right)$ with $f \left(x\right) = {x}^{3}$ and $g \left(x\right) = \cos \left(x\right)$.
Since $f ' \left(x\right) = 3 {x}^{2}$ and $g ' \left(x\right) = - \sin \left(x\right)$, the answer follows.