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Warm-Up Find the derivative
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5-5: Bases other than e Objectives:
Differentiation & integration of bases other the e Applications of exponential functions ©2003 Roy L. Gover (
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Definition which means:
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Important Idea Remember: ln x = loge x
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In the last lesson, we learned ...
& But, what about... &
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Important Idea Proof:
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Important Idea Chain Rule Version Proof:
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Compare with Note: ln a is a constant factor
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Example Find the derivative:
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Try This Find the derivative:
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Important Idea Chain Rule Version
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Example Find the derivative:
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Try This Find the derivative: Hint:
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Try This Find the derivative:
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Important Idea Proof:
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Example Find the antiderivative:
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Try This Find the antiderivative:
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Important Idea The power rule (Theorem 2-3, page 116) is now expanded to include irrational numbers.
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Assignment / 1-13 Odd, Odd, 43, all
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Example Find the derivative
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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.
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Review
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Review
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Integrals of Inverse Trig Functions:
Important Idea Integrals of Inverse Trig Functions:
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Example Evaluate: Are these integrals the same?
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Try This Evaluate: Hint: let a2=3 & u2=4x2
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Example Evaluate:
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Example Evaluate:
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Try This Evaluate: Hint: Rewrite as the sum of two quotients
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