Chain Rule
In this lesson on the chain rule, you learn how to take the derivative of a composition of functions. The chain rule is used when you have a function that is made up of multiple functions, and it allows you to take the derivative of the outer function while also taking into account the derivative of the inner function. You also learn how to apply the chain rule repeatedly, as well as how to use it in conjunction with the product rule. The cover up method is also introduced as a helpful tool for taking derivatives using the chain rule.
Know and be able to apply the derivative rule for the composition of functions (chain rule) including understanding the mixed Leibniz/prime notation used to express the chain rule.
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- What is the chain rule for taking derivatives?
- When do you use the chain rule in Calculus?
- What is the derivative of x^2?
- How can you take the derivative of (3x^2 + 2x + 1)^2 using the chain rule?
- How do you take the derivative of a composition of functions?
- If h(x) = 3x^2 + 2x + 1, and f(u) = u^2, what is the derivative of f(h(x))?
- How do you take the derivative of ((2x + 1)^2 + 2x + 1)^2?
- How do you take the derivative of (2x + 1)^2*(3x + 7)^3?
- How can you use the product rule to take the derivative of two functions multiplied together?
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Staff Review
This lesson explains the concept of the chain rule for taking the derivative of a function in Calculus. A couple of examples are shown and explained. This is an excellent place to start to learn how to use the chain rule when taking derivatives in Calculus.
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