7.2The Natural Logarithmic and Exponential Function Math 6B Calculus II.

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The Natural Logarithmic Function

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Presentation transcript:

7.2The Natural Logarithmic and Exponential Function Math 6B Calculus II

The Natural Logarithmic Function

The Derivative of y = ln x

Properties of Natural Logarithms Product Rule Quotient Rule Power Rule Domain and Range

Limits of Natural Logarithms

The Integrals of 1/x, tan x,and cot x

Logarithmic Differentiation How to Differentiate y = f (x) > 0 by Logarithmic Differentiation Take the log of both sides of the equation Differentiate both sides d/dx (ln y) = 1/y *dy/dx Solve for dy/dx Substitute y = f (x)

Laws of Exponents

The Natural Exponential Function

Properties of the Natural Exponential Function

Differentiation of e x

Integration