1. Warm Up – NO CALCULATOR Find the derivative of y = x2 ln(x3)
A particle moves along the x-axis so that at any time t > 0 its velocity is given by v(t) = tlnt – t.
Write an expression for the acceleration of the particle.
For what values of t is the particle moving to the right?

2. Derivatives of logb and Logarithmic Differentiation

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

4. Examples
Find the derivative.

5. 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.

6. Why would you want to do that?
Reason #1
Take the derivative of

7. 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.

8. Your Turn 
Use logarithmic differentiation to determine the derivative of

9. Why would you want to do that?
Reason #2
Whenever you have an x in the exponent

10. You again!
Find the derivative of