1 Derivatives of Trigonometric Functions Q. Where did the formulas for the derivatives of sinx and cosx come from? A1. Graphically: Lecture 22

2 A2. By the Definition of the Derivative: Q. Where did the formulas for the derivatives of sinx and cosx come from?

3 Derivative of the Sine Generalized Rule Ex.

4 Derivative of the Cosine Generalized Rule Ex.

5 Derivative of the Tangent Generalized Rule Ex.

6 Derivative of the Secant Generalized Rule Ex.

7 Derivative of the Cosecant Generalized Rule Ex.

8 Derivative of the Cotangent Generalized Rule Ex.

9 Derivatives Ex.

10 Derivatives Ex. Implicit differentiation

11 Problem 53 on page 562 (similar to Section 9.2 Problem. 54) 53. CostThe cost in dollars of Dig-In brand shovels is given by where t is time in years since January 1, How fast, in dollars per week, is the cost increasing each October 1?

12 Solution: Given: Find:How fast, in dollars per week, is the cost increasing each Oct. 1? That is,