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Product rule review

Review your knowledge of the Product rule for derivatives, and use it to solve problems.

What is the Product rule?

The Product rule tells us how to differentiate expressions that are the product of two other, more basic, expressions:
Basically, you take the derivative of f multiplied by g, and add f multiplied by the derivative of g.
Want to learn more about the Product rule? Check out this video.

What problems can I solve with the Product rule?

Example 1

Consider the following differentiation of h(x)=ln(x)cos(x):
=h(x)=ddx(ln(x)cos(x))=ddx(ln(x))cos(x)+ln(x)ddx(cos(x))Product rule=1xcos(x)+ln(x)(sin(x))Differentiate ln(x) and cos(x)=cos(x)xln(x)sin(x)Simplify

Check your understanding

Problem 1

Want to try more problems like this? Check out this exercise.

Example 2

Suppose we are given this table of values:
4413   08
H(x) is defined as f(x)g(x), and we are asked to find H(4).
The Product rule tells us that H(x) is f(x)g(x)+f(x)g(x). This means H(4) is f(4)g(4)+f(4)g(4). Now let's plug the values from the table in the expression:

Check your understanding

Problem 1
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Want to try more problems like this? Check out this exercise.

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