Derivatives of Logarithmic Functions Objective: Obtain derivative formulas for logs.

Review Laws of Logs Algebraic Properties of Logarithms 1.Product Property 2.Quotient Property 3.Power Property 4.Change of base

Definitions to Remember

Example 1 Does the graph of y = lnx have any horizontal tangents?

Example 1 Does the graph of y = lnx have any horizontal tangents? The answer is no. 1/x will never equal zero, so there are no horizontal tangent lines.

Example 2 Find

Example 3 Find

Absolute Value Lets look at If x > 0, |x| = x, so we have If x < 0, |x|= -x, so we have So we can say that

Example 4 Find

Example 5 Find

Example 5 Find We will use our rules of logs to make this a much easier problem.

Example 5 Now, we solve.

Logarithmic Differentiation This is another method that makes finding the derivative of complicated problems much easier. Find the derivative of

Logarithmic Differentiation Find the derivative of First, take the natural log of both sides and treat it like example 3.

Logarithmic Differentiation Find the derivative of First, take the natural log of both sides and treat it like example 3.

Logarithmic Differentiation Find the derivative of

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