Proving double derivatives with the chain rule (I think?) Hey StackExchange I'm having trouble understating where to start with this problem, I'm supposed to prove something about double derivatives and the chain rule but I'm having trouble understanding exactly what I'm being asked and how to go about doing it.
If $y = f(u)$ and $u = g(x)$, where f and g are twice differentiable functions show that:
$$\frac{d^2y}{dx^2} = \frac{d^2y}{du^2}\left(\frac{du}{dx}\right)^2 + \frac{dy}{du}\left(\frac{d^2u}{dx^2}\right)$$

The first derivative $\frac{dy}{dx}$ can be calculated with the chain rule:
$$\frac{dy}{dx}= f'(u)\cdot u' = \frac {dy}{du} \cdot \frac{du}{dx}$$
Now you need to apply the product rule and chain rule to find the second derivative.
