1. AP Calculus I 2.4 Chain Rule St. Pius X High School Ms. Hernandez AP Calculus I F06 Q1 Derivatives Unit

2. Sine and Cosine

3. Product

4. Quotient Lo de hi – Hi de lo

5. More Trig Diff Rules

6. Higher Order Derivatives First derivative y’ dy/dx Second derivative y’’ d 2 y/dx Third derivative y’’’ d 3 y/dx Fourth derivative y’’’’ d 4 y/dx y (4) …….

7. f(x) = e x and f(x) = ln(x)

8. Chain Rule y = f(g(x)) = f(u) y’=f’(u) u’ Outer function Inner function

9. Composition Functions y=f(g(x)) y= sin2x y=tan 2 x y=(x 2 -1) 1/3 y=f(u) y=sin u y=u 2 y=u 1/3 u = g(u) u=2x u= tan x u= x 2 -1

10. General Power Rule Special case of chain rule p129 f(x)=(3x-2x 2 ) 3 f’(x)=3(3x-2x 2 ) 2 (3-4x)

11. Trig & Chain Rule p132 Trig function d/dx rules Parenthesis Rewriting Trig Powers

12. Summary of Rules p133 Memorize them all

13. 2.4 Examples #15 #19 #27 #31

14. #15

15. #17

16. #27

17. #31