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The Logarithmic differentiation exercise appears under the Differential calculus Math Mission on Khan Academy. This exercise shows how to take the derivative of logarithmic functions.

Types of Problems Edit

Log diff 1

There are three types of problems in this exercise:

  1. Find the derivative of the logarithmic function: The student is asked to find the derivative of the logarithmic function and then evaluate the derivative at a certain point.
  2. Find the derivative of special powers: The student is asked to find the derivative of a function that is to the power of x by using logarithmic substitution and then evaluate the derivative at a certain point.
  3. Find the rule for the logarithmic differentiation: The student is asked to find the rules that apply to finding the derivative of the logarithmic function.

Strategies Edit

Knowledge of logarithmic differentiation concepts are encouraged to ensure success on this exercise.

Log diff 2
  1. The derivative of y=ln(x) is \frac{1}{x}
  2. The derivative of y=x^x is y(ln(x)+1)
  3. The derivative of y=x^{(x^x)} is y((x^x(ln(x)+1)ln(x)+x^{(x-1)})
  4. The value of ln(\frac{a}{b}) is equal to ln(a)-ln(b)
  5. The derivative of y=(x+a)^b(x+c)^d is y((\frac{b}{x+a}))+(\frac{d}{x+c})))


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