Presentation on theme: "Warm Up Sketch the graph of y = ln x What is the domain and range?"— Presentation transcript:
1Warm 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
10Logarithmic 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.
11Why would you want to do that? Reason #1Take the derivative of
12Let’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.
13Your Turn Use logarithmic differentiation to determine the derivative of
14To determine the derivatives of logb (not ln), use the change of base formula to change it to ln.