1. Derivatives
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2. Basic Derivatives
More Derivatives
Word Problems
Chain Rule Implicit
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3. Find the derivative of the given function using the limit definition.
Question
Find the derivative of the given function using the limit definition.

4. Answer 1 – 10

5. Find the derivative of the given function using the limit definition.
Question
Find the derivative of the given function using the limit definition.

6. Answer 1 – 20

7. Find the derivative of the given function using the power rule.
Question
Find the derivative of the given function using the power rule.

8. Answer 1 – 30

9. Find the derivative of the given function using the power rule.
Question
Find the derivative of the given function using the power rule.

10. Answer 1 – 40

11. Question
Find the equation of the tangent line at the point (1, 8) on the given function.

12. Answer 1 – 50

13. Find the derivative of the given function using the product rule.
Question
Find the derivative of the given function using the product rule.

14. Answer 2 – 10

15. Find the derivative of the given function using the product rule.
Question
Find the derivative of the given function using the product rule.

16. Answer 2 – 20

17. Find the derivative of the given function using the quotient rule.
Question
Find the derivative of the given function using the quotient rule.

18. Answer 2 – 30

19. Find the fourth derivative of the given function.
Question
Find the fourth derivative of the given function.

20. Answer 2 – 40

21. Find the average rate of change of y with respect to x over [3, 5]
Question
Find the average rate of change of y with respect to x over [3, 5]
Find the instantaneous rate of change of y with respect to x when x = -4.

22. Answer 2 – 50 Average Rate of Change over [3, 5]: 8
Instantaneous Rate of Change when x = -4: -8

23. Write the velocity and acceleration functions.
Question
An astronaut standing on the moon throws a rock into the air. The height of the rock is given by the equation below, where s is measured in feet and t is measured in seconds.
Write the velocity and acceleration functions.

24. Answer 3 – 10

25. Question
An astronaut standing on the moon throws a rock into the air. The height of the rock is given by the equation below, where s is measured in feet and t is measured in seconds.
Find how long it takes for the rock to reach its highest point. (Hint: Velocity is zero)

26. Answer 3 – 20
5 seconds

27. A rock is dropped from a height of 576 feet and falls towards Earth.
Question
A rock is dropped from a height of 576 feet and falls towards Earth.
Write the position function and identify approximately how long it takes for it to reach the ground.

28. Answer 3 – 30
6 seconds

29. A rock is dropped from a height of 576 feet and falls towards Earth.
Question
A rock is dropped from a height of 576 feet and falls towards Earth.
What is the average velocity of the rock during the time it is falling?

30. Answer 3 – 40
-96 feet/second

31. A rock is dropped from a height of 576 feet and falls towards Earth.
Question
A rock is dropped from a height of 576 feet and falls towards Earth.
What is the instantaneous velocity of the rock when it hits the ground?

32. Answer 3 – 50
-192 feet/second

33. Find the derivative of the given function using the chain rule.
Question
Find the derivative of the given function using the chain rule.

34. Answer 4 – 10

35. Find the derivative of the given function using the chain rule.
Question
Find the derivative of the given function using the chain rule.

36. Answer 4 – 20

37. Find the derivative of the given function using the chain rule.
Question
Find the derivative of the given function using the chain rule.

38. Answer 4 – 30

39. Find the derivative implicitly.
Question
Find the derivative implicitly.

40. Answer 4 – 40

41. Question
Find the derivative implicitly. Then determine the slope of the tangent at the indicated point.

42. Answer 4 – 50

43. Question
Find the derivative implicitly. Then determine the slope of the tangent at the indicated point.

44. Answer 5 – 10

45. Use the following equation and information to answer the question.

46. Answer 5 – 20

47. Question
A spherical balloon is inflated so that its volume is increasing at a rate of 3 ft3/min. How fast is the radius of the balloon increasing when the radius is 1 foot?

48. Answer 5 – 30

49. Question
A fire has started in a dry, open field and spreads in the form of a circle. The radius of the circle increases at a rate of 6 ft/min. Find the rate at which the fire area is increasing when the radius is 150 feet.

50. Answer 5 – 40

51. Question
As sand leaks out of a hole in a container, it forms a conical pile whose altitude is always the same as the radius. If the height of the pile is increasing at a rate of 6 in/min, find the rate at which the sand is leaking out when the altitude is 10 inches.

52. Answer 5 – 50