Learning the chain rule is best done through practice. After a few examples, you'll get the hang of it. You'll want it to become second-nature, because finding derivatives quickly and accurately is a necessary first step in much of the calculus still ahead. These examples might help you along. They start easier and get more difficult as you go.

1. Simple chain rule examples

Here are a few examples of taking derivatives of simpler compound functions:

• f(x) = cos(x³),
• g(x) = tan(1/x), and
• h(x) = e^3x-1

Minutes of your life: 3:22

 

2. More difficult chain rule examples

These are just a little bit more difficult. Notice that it's called the chain rule because we can use it to find derivatives of a function of a function of a function of ..., like f(g(h(x))) = tan(ln(x²)), where f(x) = tan(x), g(x) = ln(x) and h(x) = x².

Minutes of your life: 3:22

 

3. Challenging chain rule derivatives

If you can find derivatives of functions like these, you'll have mastered the chain rule.

Minutes of your life: 3:22

 

 
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