Differentiation Rules for Logarithmic Functions

In this tutorial we shall discuss the 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 the general logarithmic formulae when any functions are of the following forms are:

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

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