Derivative rule of the Natural Logarithmic function

Formula

$\dfrac{d}{dx}{\log_{e}{x}} \,=\, \dfrac{1}{x}$

Introduction

If $x$ is a variable, then natural logarithm is denoted by either $\ln{(x)}$ or $\log_{e}{(x)}$. The derivative of natural logarithm with respect to $x$ is equal to the quotient of one by $x$.

Proof

Learn how to derive differentiation of natural logarithm with respect to $x$ in differential calculus by the limit definition of derivative.