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Could someone explain Chain Rule, Derivatives, and the Quotient Rule? Thanks.
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This could be a long post.
I'll rewrite my question. What are they used for?
The chain rule and the quotient rule are rules or processes for that matter that are used to calculate derivatives. Derivatives are used for various things, most common and applicable is rates. Derivatives define a rate of change with respect to something like time. So for example, acceleration is the derivative of velocity and quantifies the rate at which the velocity is changing. Other typical calc one types of things derivatives are used for is finding max and minimum values of functions etc.
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