When two functions $f(x)$ and $g(x)$ are multiplied together, we get a new function, which we may call $h(x)$:

If we can find the gradient of $f$ and $g$, we would like to be able to find the gradient of $h$. Fortunately, the product rule can help:

We will get used to using this rule, and in a later problem we will prove that it works.

1. Let

   $$h(x)=(x^2-3x)\sin (x)$$

   Find $h^{\prime }(x)$

2. Let

   $$y=\sqrt{x}{e}^{2x}$$

   Find $\frac{dy}{dx}$ and $\frac{d^{2}y}{d{x}^2}$