Presentation on theme: "Warm Up 1)Sketch the graph of y = ln x a)What is the domain and range? b)Determine the concavity of the graph. c)Determine the intervals where the graph."— Presentation transcript:
Warm Up 1)Sketch the graph of y = ln x a)What is the domain and range? b)Determine the concavity of the graph. c)Determine the intervals where the graph is increasing. Evaluate each without using a calculator. 2) log ) ln e 4 5) log
Derivatives involving ln and log b
“The derivative of ln of something is… one over the something times the derivative of the something.” Derivative involving natural logs.
Examples Find the derivative.
Find the derivative of y = x 2 ln(x 3 )
Write the equation of the tangent line to y = ln (x 1/2 ) at the point where x = 1
Sometimes it is easier to find a derivative if you use properties to simplify first. Find the derivative of
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. Logarithmic Differentiation…
Why would you want to do that? Reason #1 Take the derivative of
Let’s Review the steps… 1.Take ln of both sides. 2.Simplify the right side using log properties. 3.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.
Your Turn Use logarithmic differentiation to determine the derivative of
To determine the derivatives of log b (not ln), use the change of base formula to change it to ln.