Chapter 2.3, Problem 87E

 (a) Use the Product Rule twice to prove that if f, g, and h are differentiable, then $\left(fgh\right)\prime =f\prime gh+fg\prime h+fgh\prime$.

(b) Taking $f=g=h$ in part (a), show that

$\frac{d}{dx}{\left[f\left(x\right)\right]}^3=3{\left[f\left(x\right)\right]}^{2}f\prime \left(x\right)$

(c) Use part (b) to differentiate $y={\left(x^4+3x^3+17x+82\right)}^3$.