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13.5 Day 1 Chain Rule for Functions of Several Variables

13.5 Day 1 Chain Rule for Functions of Several Variables. If is the composite of and , then:. Find:. example:. From Calc AB. Chain Rule:. We could also do it this way:. Evaluate at x=2. Example 1. How do you think we should do this problem?.

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13.5 Day 1 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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