Calculus I: Derivatives
Logarithmic differentiation

Logarithmic Differentiation

Taking the derivatives of some complicated functions can be simplified by using logarithms. This is called logarithmic differentiation.

y = f(x)

This technique is done in three steps:

• Take the ln of the two sides of the equation ln(y) = ln (f(x))
• Differentiate the two sides with respect to x to obtain:
(dy/dx)/y = d(ln (f(x)))/dx
• Explicit y'

Example

y = x^x

• ln (y) = x ln (x)
• y'/y = ln(x) + 1
• y' = x^x (ln(x) + 1 )