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Presentation transcript:

Quick Review

Quick Review Solutions

Quick Review

Quick Review Solutions

Derivatives of Exponential and Logarithmic Functions 3.9 Derivatives of Exponential and Logarithmic Functions

What you’ll learn about Derivative of ex Derivative of ax Derivative of ln x Derivative of logax Power Rule for Arbitrary Real Powers … and why The relationship between exponential and logarithmic functions provides a powerful differentiation tool called logarithmic differentiation.

Derivative of ex

Example Derivative of ex

Derivative of ax

Derivative of ln x

Example Derivative of ln x

Derivative of logax

Rule 10 - Power Rule For Arbitrary Real Powers If u is a positive differentiable function of x and n is a real number, then

Example Power Rule For Arbitrary Real Powers

Logarithmic Differentiation Sometimes the properties of logarithms can be used to simplify the differentiation process, even if logarithms themselves must be introduced as a step in the process. The process of introducing logarithms before differentiating is called logarithmic differentiation.

Example Logarithmic Differentiation

Example Logarithmic Differentiation

Quick Quiz Sections 3.7 – 3.9

Quick Quiz Sections 3.7 – 3.9

Quick Quiz Sections 3.7 – 3.9

Quick Quiz Sections 3.7 – 3.9

Quick Quiz Sections 3.7 – 3.9

Quick Quiz Sections 3.7 – 3.9

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