1. The problem is to differentiate a function using the product rule. 2. The product rule states that if you have two functions $u(x)$ and $v(x)$, then the derivative of their product is given by: $$\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$$ 3. This means you take the derivative of the first function and multiply it by the second function as is, then add the first function multiplied by the derivative of the second function. 4. For example, if $f(x) = x^2 \sin(x)$, then let $u(x) = x^2$ and $v(x) = \sin(x)$. 5. Compute the derivatives: $u'(x) = 2x$ and $v'(x) = \cos(x)$. 6. Apply the product rule: $$f'(x) = u'(x)v(x) + u(x)v'(x) = 2x \sin(x) + x^2 \cos(x)$$ 7. This is the derivative of the product using the product rule. 8. Remember to always identify the two functions clearly and differentiate each separately before applying the formula.