What rule is used to find the derivative of a product of two functions?

The product rule is specifically designed to find the derivative of the product of two functions. When you have two differentiable functions, say ( f(x) ) and ( g(x) ), the product rule states that the derivative of their product ( f(x)g(x) ) can be computed using the formula:

[

\frac{d}{dx}[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)

]

This means you take the derivative of the first function, multiply it by the second function, and then add the first function multiplied by the derivative of the second function. This rule is important because it allows you to correctly combine the rates of change of both functions, ensuring that you account for how each function contributes to the overall product.

The other rules mentioned, such as the chain rule (used for composites of functions), the quotient rule (for the division of functions), and the sum rule (for the addition of functions) serve different purposes and are not applicable when you specifically want to differentiate the product of two functions.