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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

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.

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 $y((\frac{b}{x+a}))+(\frac{d}{x+c})))$