What is logarithmic differentiation?

Logarithmic differentiation refers to the process in calculus of finding the derivative of a function by using the properties of the natural logarithmic function. The natural logarithmic function is notated by "ln."

The general rule for logarithmic differentiation is that the derivative of the function ln(f) is equal to the derivative of f over f. Using mathematical notation, this rule reads as [ln(f)]' = f'/f, where the apostrophe indicates a derivative. For example, the derivative of the equation y = x^x can be solved by applying the natural log to both sides of the equation as ln(y) = xln(x), for a final solution of (x^x)(1 + ln(x)).