1. The Derivative: “Derivatives of Trigonometric Functions”
Section 2.5
The Derivative: “Derivatives of Trigonometric Functions”

2. All graphics are attributed to:
Calculus,10/E by Howard Anton, Irl Bivens, and Stephen Davis Copyright © 2009 by John Wiley & Sons, Inc. All rights reserved.

3. Objective
The main objective of this section is to obtain formulas for the derivatives of the six basic trigonometric functions and them use them along with the previous rules in finding derivatives.
There is a proof for the derivative of sin x on the next page. Please do not just skip that slide.  Try to follow along. You do not need to copy it down.

4. Proof

5. Derivatives of sin x, cos x, tan x
You can prove the derivatives of cos x and tan x similarly and you will have to on the test. 

6. Derivatives of csc x, sec x, cot x

7. Example
Now use those trig. derivatives along with the product, quotient, etc rules:

8. Example #2

9. Hall of Mirrors at Versailles