Logarithmic Differentiation

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 ==
There are three types of problems in this exercise:
# 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.
# 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.
# 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 ==
Knowledge of logarithmic differentiation concepts are encouraged to ensure success on this exercise.
# The derivative of y=ln(x) is \frac{1}{x}
# The derivative of y=x^x is y(ln(x)+1)
# The derivative of y=x^{(x^x)} is y((x^x(ln(x)+1)ln(x)+x^{(x-1)})
# The value of ln(\frac{a}{b}) is equal to ln(a)-ln(b)
# The derivative of y=(x+a)^b(x+c)^d is y((\frac{b}{x+a}))+(\frac{d}{x+c})))
Category:Math