LOGARITHMIC DIFFERENTIATION

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LOGARITHMIC DIFFERENTIATION

• By Dr. Eliane Keane

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Differentiate y xx

• Notice that the ordinary rules of differentiation
  do not apply
• So, what do you do?

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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.

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Solving the Problem

• y xx
• ln y ln xx (apply ln on both sides)
• ln y x ln x (use prop of logs)

( differentiate both sides)
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Continue to Solve
(simplify)
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YOU MADE IT!
No more crying
Now you try it!
1) Differentiate