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The Calculus Lifesaver by Adrian Banner

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CHAPTER 10 _____________________________

Inverse Functions and Inverse Trig Functions

In the previous chapter, we looked at exponentials and logarithms. We got a lot of mileage out of the fact that ex and ln(x) are inverses of each other. In this chapter, we’ll look at some more general properties of inverse functions, then examine inverse trig functions (and their hyperbolic cousins) in greater detail. Here’s the game plan:

• using the derivative to show that a function has an inverse;

• finding the derivative of inverse functions;

• inverse trig functions, one by one; and

• inverse hyperbolic functions.

10.1 The Derivative and Inverse Functions

In Section 1.2 of Chapter 1, we reviewed the basics of inverse functions. I strongly suggest you ...

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