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Warm-Up Find the derivative.

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Presentation on theme: "Warm-Up Find the derivative."— Presentation transcript:

1 Warm-Up Find the derivative

2 5-5: Bases other than e Objectives:
Differentiation & integration of bases other the e Applications of exponential functions ©2003 Roy L. Gover (

3 Definition which means:

4 Important Idea Remember: ln x = loge x

5 In the last lesson, we learned ...
& But, what about... &

6 Important Idea Proof:

7 Important Idea Chain Rule Version Proof:

8 Compare with Note: ln a is a constant factor

9 Example Find the derivative:

10 Try This Find the derivative:

11 Important Idea Chain Rule Version

12 Example Find the derivative:

13 Try This Find the derivative: Hint:

14 Try This Find the derivative:

15 Important Idea Proof:

16 Example Find the antiderivative:

17 Try This Find the antiderivative:

18 Important Idea The power rule (Theorem 2-3, page 116) is now expanded to include irrational numbers.

19 Assignment / 1-13 Odd, Odd, 43, all

20 Example Find the derivative

21 Warm-Up If the average annual rate of inflation is 3% over 6 years, then the cost, c, of a house in any year of that period is c(t)=p(1.03)t where p is the present cost. If the cost is $100,000 now (t=0), what is the cost in 2 years? How long will it be before the house will cost $110,000? Find the rate at which the cost is changing when t=5.

22 Review

23 Review

24 Integrals of Inverse Trig Functions:
Important Idea Integrals of Inverse Trig Functions:

25 Example Evaluate: Are these integrals the same?

26 Try This Evaluate: Hint: let a2=3 & u2=4x2

27 Example Evaluate:

28 Example Evaluate:

29 Try This Evaluate: Hint: Rewrite as the sum of two quotients


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