2. LOGARITHMIC DIFFERENTIATION By Dr. Eliane Keane

3. Differentiate y = x x Notice that the ordinary rules of differentiation do not apply… So, what do you do?

4. Solution to the Problem The following problem illustrates the process of logarithmic differentiation. It is a means of differentiating algebraically complicated functions or functions for which the ordinary rules of differentiation do not apply. For example, in this problem, you will be asked to differentiate an expression where a variable is raised to a variable power.

5. Solving the Problem y = x x ln y = ln x x (apply ln on both sides) ln y = x ln x (use prop of logs) ( differentiate both sides)

6. Continue to Solve (simplify) ( substitute back the value of y)

7. YOU MADE IT! No more crying 1) Differentiate