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AP Derivatives

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AP Derivatives

1. 1. Derivative?f(x)= sinx
2. 2. Answerf(x)= cosx
3. 3. Derivative?xxf1)( =
4. 4. Answer21)(xxf −=
5. 5. What does this mean??lim0=−+→ hee xhxh
6. 6. Answer:It is asking for thederivative of ex. Thenotation is the limitdefinition of the derivative(difference quotient)
7. 7. Derivative?)()(xgxfy =
8. 8. Answer-Quotient Rule( )LowLowHighDLowLowDHighyxgxgxfxfxgy−=−=)()()()()( 2
9. 9. Derivative?f(x)= ax
10. 10. Answeraaxf xln)( =
11. 11. Derivative?f(x)= cotx
12. 12. Answerf(x)= -csc2x
13. 13. Derivative?f(x)= secx
14. 14. Answerf(x)= secxtanx
15. 15. Derivative?f(x)= arctanx= tan-1x
17. 17. Derivative?f(x)= cosx
18. 18. Answerf(x)= -sinx
19. 19. Derivative?f(x)= ex
20. 20. Answerf(x)= ex
21. 21. Derivative?f(x)= arccosx= cos-1x
23. 23. Derivative?f(x)= tanx
24. 24. Answerf(x)= sec2x
25. 25. Derivative?f(x)= arccscx= csc-1x
27. 27. Derivative?f(x)= lnx
28. 28. Answerxxf1)( =
29. 29. Derivative?f(x)= cscx
30. 30. Answerf(x)= -cscxcotx
31. 31. Derivative?y=f(x)g(x)
32. 32. Answer-Product Ruley= f(x)g(x)+f(x)g(x)
33. 33. Derivative?f(x)= arcsinx= sin-1x
35. 35. Derivative?f(x)= arccotx= cot-1x