Calculus – Product Rule

The product rule is used to find the derivative of the product of two functions.

The Product Rule

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) and v = g(x) then

Example:

Find f’(x) if f(x) = (6x³)(7x⁴)

Solution:

Using the Product Rule, we get

Example:

Given f(x) = (3x² – 1)(x² + 5x +2), find the derivative of f(x).

Solution:

Using the Product Rule, we get

Videos

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.

The Product Rule for Derivatives

Examples using the Product Rule and Chain Rule.

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