The Product Rule

SUMMARY Otherwise use the product rule: If where u and v are both functions of x To differentiate a product: Check if it is possible to multiply out. If so, do it and differentiate each term.

Let e.g. and Remove common factors:

We can now differentiate all of the following: A simple function could be like any of the following: We differentiate them term by term using the 4 rules for The multiplying constants just “tag along”. simple functions, products and

Decide how you would differentiate each of the following ( but don’t do them ): Product rule Chain rule This is a simple function For products we use the product rule and for functions of a function we use the chain rule.

It can be tricky to distinguish between products and functions of a function. If you do have difficulty try the following: Assume you have a product. Then, you must have 2 factors ( at least ). If you can’t then it isn’t a product. Try to split up the function into one function multiplied by another.