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Calculus Chain Rule for Functions of Several Variables

Learn how to apply the chain rule for composite functions in calculus, with examples and solutions. Practice evaluating functions and finding rates of change.

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Calculus Chain Rule for Functions of Several Variables

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  1. 13.5 Day 1 Chain Rule for Functions of Several Variables

  2. If is the composite of and , then: Find: example: From Calc AB Chain Rule:

  3. We could also do it this way: Evaluate at x=2

  4. Example 1 How do you think we should do this problem? Solve via substitution

  5. Now we can do example 1 without first doing a substitution

  6. Solution to Example 1

  7. Example 2 Two objects are traveling in elliptical paths given by the parametric equations given below. What is the rate of change of the distance between the objects when t = π? Hint use the Chain rule:

  8. Example 2 Solution Solution: You can see that the distance s between the two objects is given by

  9. Example 2 solution continued

  10. Example 3 Find the answer by using substitution

  11. Example 3 solution 1

  12. We can now do example 3 without first having to do a substitution

  13. There are some things that you Just need to memorize!!!

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