1. The problem: Learn the product rule for differentiation. 2. The product rule states that if you have two functions $u(x)$ and $v(x)$, the derivative of their product is given by: $$\frac{d}{dx}[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)$$ 3. Explanation: To differentiate a product of two functions, you differentiate the first function and multiply it by the second function as it is, then add the first function multiplied by the derivative of the second function. 4. Example: Suppose $u(x) = x^2$ and $v(x) = \sin(x)$. - First, find $u'(x) = 2x$. - Then, find $v'(x) = \cos(x)$. 5. Apply the product rule: $$\frac{d}{dx}[x^2 \sin(x)] = 2x \sin(x) + x^2 \cos(x)$$ 6. This is the derivative of the product of $x^2$ and $\sin(x)$. 7. Remember: The product rule helps you differentiate products of functions by taking the derivative of each function separately and combining them as shown.