1. Derivative?
f(x)= sinx

2. Answer
f'(x)= cosx

3. Derivative?
x
xf
1
)( =

4. Answer
2
1
)('
x
xf −=

5. What does this mean?
?lim
0
=
−+
→ h
ee xhx
h

6. Answer:
It is asking for the
derivative of ex
. The
notation is the limit
definition of the derivative
(difference quotient)

7. Derivative?
)(
)(
xg
xf
y =

8. Answer-Quotient Rule
( )
LowLow
HighDLowLowDHigh
y
xg
xgxfxfxg
y
−
=
−
=
'
)(
)(')()(')(
' 2

9. Derivative?
f(x)= ax

10. Answer
aaxf x
ln)(' =

11. Derivative?
f(x)= cotx

12. Answer
f'(x)= -csc2
x

13. Derivative?
f(x)= secx

14. Answer
f'(x)= secxtanx

15. Derivative?
f(x)= arctanx= tan-1
x

16. Answer
2
1
1
)('
x
xf
+
=

17. Derivative?
f(x)= cosx

18. Answer
f'(x)= -sinx

19. Derivative?
f(x)= ex

20. Answer
f'(x)= ex

21. Derivative?
f(x)= arccosx= cos-1
x

22. Answer
2
1
1
)('
x
xf
−
−=

23. Derivative?
f(x)= tanx

24. Answer
f'(x)= sec2
x

25. Derivative?
f(x)= arccscx= csc-1
x

26. Answer
1||
1
)('
2
−
−=
xx
xf

27. Derivative?
f(x)= lnx

28. Answer
x
xf
1
)(' =

29. Derivative?
f(x)= cscx

30. Answer
f'(x)= -cscxcotx

31. Derivative?
y=f(x)g(x)

32. Answer-Product Rule
y'= f'(x)g(x)+f(x)g'(x)

33. Derivative?
f(x)= arcsinx= sin-1
x

34. Answer
2
1
1
)('
x
xf
−
=

35. Derivative?
f(x)= arccotx= cot-1
x

36. Answer
2
1
1
)('
x
xf
+
−=

37. Derivative?
f(x)= arcsecx= sec-1
x

38. Answer
1||
1
)('
2
−
=
xx
xf

39. Derivative?
xxf alog)(' =

40. Answer
ax
xf
ln
1
)(' =

41. Derivative?
y= f(g(x))

42. Answer-Chain Rule
y'= f'(g(x))g'(x)

43. dy=?

44. Answer
dy=f’(x)dx

45. y=?

46. Answer
y=f(x+ x)-f(x)

47. Derivative of Inverse

48. Answer
)('
1
)(' 1
yf
xf −
=