Warm-Up Find the derivative.

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Presentation transcript:

Warm-Up Find the derivative

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

Definition which means:

Important Idea Remember: ln x = loge x

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

Important Idea Proof:

Important Idea Chain Rule Version Proof:

Compare with Note: ln a is a constant factor

Example Find the derivative:

Try This Find the derivative:

Important Idea Chain Rule Version

Example Find the derivative:

Try This Find the derivative: Hint:

Try This Find the derivative:

Important Idea Proof:

Example Find the antiderivative:

Try This Find the antiderivative:

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

Assignment 1. 366/ 1-13 Odd, 25-39 Odd, 43, 60-66 all

Example Find the derivative

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.

Review

Review

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

Example Evaluate: Are these integrals the same?

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

Example Evaluate:

Example Evaluate:

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