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How to use the product rule is used to find the derivative of the product of two functions?

### What is The Product Rule?

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Product Rule

Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functions.

Product rule, step by step, derivative example.
The Product Rule for Derivatives

Examples using the Product Rule and Chain Rule.
Derivatives - Product + Chain Rule + Factoring

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More Lessons for Calculus, Math Worksheets

How to use the product rule is used to find the derivative of the product of two functions?

The Product Rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function times the derivative of the first function.

If *f* and *g* are both differentiable, then

You may want to remember the Product Rule as follows:

Let

u=f(x) andv=g(x) then

*Example: *

Find *f’*(*x*) if *f*(*x*) = (6*x*^{3})(7*x*^{4})

**Solution:**

Using the Product Rule, we get

**Example:**

Given *f*(*x*) = (3*x*^{2 }– 1)(x^{2} + 5x +2), find the derivative of *f*(*x*).

**Solution:**

Using the Product Rule, we get

Use the product rule to find the derivative of the product of two functions--the first function times the derivative of the second, plus the second function times the derivative of the first. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functions.

Product rule, step by step, derivative example.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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