**Definition**: Given two differentiable functions, *f*(*x*) and *g*(*x*), the derivative of *f*(*x*)*g*(*x*) is *f*‘(*x*)*g*(*x*)+*g*‘(*x*)*f*(*x*).

**Example 1**: Find the derivative of $h(x) = x^2 \sin(x)$.

**Solution:** This looks like a product of two functions, so let’s break it up. Let and let $g(x) = \sin(x)$; then . We first find the derivatives of these two functions:

Then we use the product rule:

**Example 2**: Find the derivative of .

**Solution:** First, we can break *p*(*x*) up into three functions: . Then, find the derivatives of each of these functions:

Now, consider *p*(*x*) as two functions: *f*(*x*)*g*(*x*) and *h*(*x*). To find the derivative of *f*(*x*)*g*(*x*), we use the product rule:

Then, we can take the derivative of the entire function:

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