Math Doubts

Derivative of Natural Logarithm

Formula

$\dfrac{d}{dx}{\ln{x}}$ $\,=\,$ $\dfrac{1}{x}$

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.

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