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Chain Rule

There are two big parts to mastering the Chain Rule:

  1. Identify the chain rule is necessary.
  2. Use the chain rule by taking the derivative of the outside function, then the inside function.

We use the chain rule to take the derivative of a function with two components.

f'(g(x)) = f'(g(x)) * g'(x)

Common functions requiring Chain Rule:

sin^2 x \frac{1}{cos x} \frac{1}{e^x}

How to master:

  1. Watch two of the three videos below that explain the Chain Rule with examples.
  2. Complete the worksheet of quick practice to get down the steps.
  3. Use quick practice to state whether Chain Rule is necessary.

Maintenance: Be sure you can quickly identify whether Chain Rule applies to functions.

NancyPi Describes Chain Rule


Organic Chemistry Tutor provides examples of the Chain Rule


Khan Academy has a great overview of the Chain Rule

Distrust Authority?

This hands-on example shows how the chain rule works using wheels representing each function: