Differentiation Rules for Logarithmic Functions

In this tutorial we discuss basic differentiation formulas of logarithmic functions.

1. \frac{d}{{dx}}\ln x = \frac{1}{x},\,\,\,x > 0

2. \frac{d}{{dx}}{\log _a}x = \frac{1}{{x\ln  a}},\,\,\,\,a > 0,\,\,\,a \ne 1

Now general logarithmic formulae when any function, the following formulas are of the form 

 1. \frac{d}{{dx}}\ln f\left( x \right) =  \frac{1}{{f\left( x \right)}}\frac{d}{{dx}}f\left( x \right)

2. \frac{d}{{dx}}{\log _a}f\left( x \right) =  \frac{1}{{f\left( x \right)\ln a}}\frac{d}{{dx}}f\left( x \right),\,\,\,\,a  > 0,\,\,\,a \ne 1