Differentiation rules > Product rule
123456Product rule

## Theory

To find the derivative of a function that is the product of two functions you can use:

Differentiation rule (product rule):
If $P\left(x\right)=f\left(x\right)\cdot g\left(x\right)$ then $P\text{'}\left(x\right)=f\text{'}\left(x\right)\cdot g\left(x\right)+f\left(x\right)\cdot g\text{'}\left(x\right)$.

This rule is not always necessary. Often you can rewrite a function without parentheses.
But when, for instance, one function is a quadratic function and the other one an exponential function, you really need this product rule.

Often you need to use this rule in combination with the preceding rules. Especially the chain rule shows up a lot!