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The Calculus Lifesaver by Adrian Banner

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CHAPTER 8 ______________________________

Implicit Differentiation and Related Rates

Let’s take a break from trying to work out how to differentiate everything in sight. It’s time to look at implicit differentiation, which is a nice generalization of regular differentiation. We’ll then see how to use this technique to solve word problems involving changing quantities. Knowing how fast one quantity is changing allows us to find how fast a different, but related, quantity is changing too. Anyway, the summary for this chapter is the same as the title:

• implicit differentiation; and

• related rates.

8.1 Implicit Differentiation

Consider the following two derivatives:

The first is just 2x, as we’ve seen. So isn’t the second one 2y? That would be ...

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