# How do you find the derivative of y=6 cos(x^3+3) ?

This is a composite of the function ${x}^{3} + 3$ and the function $6 \cos x$, so we will need the Chain Rule together with $\left({x}^{3} + 3\right) = 3 {x}^{2}$ and $\left(\cos x\right) ' = - \sin x$ (as shown here:derivative of trig functions ).
$\left(6 \cos \left({x}^{3} + 3\right)\right) ' = - 6 \sin \left({x}^{3} + 3\right) \setminus \times \left({x}^{3} + 3\right) ' = - 18 {x}^{2} \sin \left({x}^{3} + 3\right)$.