Chapter 2.5, Problem 89E

If $y=f(u)$ and $u=g(x)$, where f and g are twice differentiable functions, show that

$\frac{d^2}{d{x}^2}=\frac{d^2}{d{u}^2}{\left(\frac{du}{dx}\right)}^2+\frac{dy}{du}\frac{d^{2}u}{d{x}^2}$