This week in class we focused primarily on the Chain Rule. It is the 7th rule of derivatives and is one of the most important.
Equation-
Application-
Every time there is a function nested inside of another function the chain rule is extremely useful. It is used to link parts of equations together and for differentiating complicated equations. It allows people to take derivatives of much more complex problems.
Explanation-
To take the derivative you have to look at the most outside function, usually an exponent. Just pretend that the inside is just an x as usual and take the derivative and leave the inside portion unchanged, but still copy it down. Then multiply that answer by the derivative of the stuff on the inside that you previously ignored. That is the basics of the rule, but this process may have to be repeated depending on the extent of the problem.
Practice Problems-
Using the Rule Twice in Same Problem-
Finding dr/d(theta)
More Complicated Problem-
Using Values From a Table-
Tips-
- Always work from the outside in
- Anytime there is a nested function, think to use the chain rule
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