1. Consider the function We could make a graph of the slope: slope Now we connect the dots! The resulting curve is a cosine curve. 2.3 Derivatives of Trigonometric Functions

2. Proof

3. 2.3 Derivatives of Trigonometric Functions = 0 = 1

4. 2.3 Derivatives of Trigonometric Functions Find the derivative of cos x

5. 2.3 Derivatives of Trigonometric Functions = 0 = 1

6. We can find the derivative of tangent x by using the quotient rule. 2.3 Derivatives of Trigonometric Functions = = = = =

7. Derivatives of the remaining trig functions can be determined the same way. 2.3 Derivatives of Trigonometric Functions

9. Chain Rule: 2.4 Chain Rule Let h(x) = f(g(x)) (also known as ) Then h(x) = (f(g(x)) =

10. Here is a faster way to find the derivative: Differentiate the outside function... …then the inside function 2.4 Chain Rule

11. The chain rule can be used more than once. (Thats what makes the chain in the chain rule!) 2.4 Chain Rule = = = = =

12. Derivative formulas include the chain rule! etcetera… 2.4 Chain Rule

13. Find