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Published byTerrence Roylance Modified over 3 years ago

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**Warm Up Sketch the graph of y = ln x What is the domain and range?**

Determine the concavity of the graph. Determine the intervals where the graph is increasing. Evaluate each without using a calculator. 2) log ) ln e ) log

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Homework Questions…

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**Derivatives involving ln and logb**

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**Derivative involving natural logs.**

“The derivative of ln of something is… one over the something times the derivative of the something.”

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Examples Find the derivative.

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**Find the derivative of y = x2 ln(x3)**

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**Write the equation of the tangent line to y = ln (x1/2) at the point where x = 1**

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**Sometimes it is easier to find a derivative if you use properties to simplify first.**

Find the derivative of

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Find the derivative of

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**Logarithmic Differentiation…**

All it means is that you have something you want to differentiate, you take the natural log of both sides of an equation before you take the derivative.

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**Why would you want to do that?**

Reason #1 Take the derivative of

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**Let’s Review the steps…**

Take ln of both sides. Simplify the right side using log properties. Take the derivative of both sides. (You always get on the left side) 4. Move the y to the right side of the = (to solve for dy/dx) and substitute the original y equation in for y.

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Your Turn Use logarithmic differentiation to determine the derivative of

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**To determine the derivatives of logb (not ln), use the change of base formula to change it to ln.**

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Examples Find the derivative.

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