What is the product rule?

In calculus, the product rule is used to calculate the derivatives of problems where one function is multiplied by another. It is represented by the equation (f * g)' = f' * g + f * g'. In differential notation, it's written as d(uv) = u dv + v du.

The rule states that one obtains the derivative of a function multiplied by another function by first multiplying each individual function by the other function’s derivative. Other rules are applied as necessary, such as the power rule and the chain rule.

The two resulting products are then added together. Their sum is the derivative of the original two functions' product.