- Now, how do we know that
? 
So the question remains: how do we know that
? Let's rewrite it a little: we want to show that
- Here's the general situation:
- Examples:
- #1, p. 390
- #19, p. 390
- A better proof of the fact that
(take logs! Better than induction....)
- #53, p. 390
- My interest is primarily in inverting the functions sine, cosine,
and tangent. Let's start by taking a look at each of these
graphically, e.g. sine:
-
- Derivatives are obtained using the formula for inverse function
derivatives:
from which we derive:
Geometry gives us another way to derive it:
How would we cook up the geometry to derive the derivative of arctan?
- Examples:
- #50, p. 398
- #53, p. 398
- #58, p. 398
- #85, p. 399