Section 3.8

1. Section 3.8

3. Left unchecked, many things tend to grow or decay exponentially.

4. Left unchecked, many things tend to grow or decay exponentially.

5. Left unchecked, many things tend to grow or decay exponentially.

6. Left unchecked, many things tend to grow or decay exponentially.

7. Left unchecked, many things tend to grow or decay exponentially.

8. Left unchecked, many things tend to grow or decay exponentially.

9. Left unchecked, many things tend to grow or decay exponentially.

10. Left unchecked, many things tend to grow or decay exponentially.

11. Left unchecked, many things tend to grow or decay exponentially. Einstein called compound interest the most powerful force in the universe

19. or use the definition of e which is:

20. In a dark, narrow alley, a function and a differential operator meet: "Get out of my way – or I'll differentiate you till you're zero!" "Try it - I'm ex..." d/dx slinks off into the night…

21. In a dark, narrow alley, a function and a differential operator meet: "Get out of my way – or I'll differentiate you till you're zero!" "Try it - I'm ex..." d/dx slinks off into the night… • Same alley, same function, but a different differential operator: • "Get out of my way – • or I'll differentiate you till you're zero!“ • "Try it - I'm ex..." • "Too bad... I'm d/dy."

31. What about the derivative of f(x) = ln x ?

32. What about the derivative of f(x) = ln x ?

33. What about the derivative of f(x) = ln x ?

34. What about the derivative of f(x) = ln x ?

35. What about the derivative of f(x) = ln x ?

36. What about the derivative of f(x) = ln x ?

37. What about the derivative of f(x) = ln x ?

38. What about the derivative of f(x) = ln x ?

40. =

41. = =

42. = = Rule of : if the base is NOT e then for exponentials * ln a for logarithms ln a

44. This is a product.

45. This is a product.

46. This is a product.

47. This is a product.

48. Simplified means to write the answer with as few symbols as possible.

50. This is a composite…