How do you differentiate a function comprised of two functions multiplied together?

The product rule is useful when you’re dealing with a function comprised of two functions multiplied together. Generally, if you have a function of the form y = f(x)g(x), then the derivative of the function would be dy/dx = f(x)g'(x) + g(x)f'(x). As with any derivative, it is easiest to write it in notation that raises a variable to a power using numbers by applying the rules for indices. Once you have done this, make it clear to yourself the two different functions being multiplied together. Using the general results of differentiation, find the derivative of the second function (g’(x)) and multiply it to the first function (f(x)), then find the derivative of the first function (f’(x)) and multiply it by the second function (g(x)). When differentiating either of the two functions you may also need to apply the chain rule. An example of when the product rule could be applied would be for the following function:

y=x^2(5x-1)^1/2