The product rule is useful for differentiating the product of functions.
It states that for any functions and ,
Or, in Lagrange notation,
We begin by recalling the definition of differentiation:
Thus, we have
The product rule can also be applied to the product of numerous variables. For example,
or in Lagrange notation
Applying the product rule with and , we get that
Find the derivative of
We may recognize this as a basic property of integerals. Applying the product rule with and , we get that
Some functions may require the combined use of differentiation rules, such as this one here:
If you are having some trouble, you may want to review the chain rule.