The product rule is used for differentiating functions multiplied by each other.

\(y = f(x)g(x) \)

\(\boxed{\dfrac{dy}{dx} = f'(x)g(x) + f(x)g'(x)} \)

Using substitution, if \(u = f(x) \) and \(v = g(x) \), then:

\(\boxed{\dfrac{dy}{dx} = \dfrac{du}{dx}v + u\dfrac{dv}{dx}} \)

Tip: Think of it as "the derivative of the first function, multiplied by the second function, plus the first function multiplied by the derivative of the second function".