ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5175 on D5681: Real function derivative

Derivative function for standard natural real logarithm function

Formulation 0

Let $\log : (0, \infty) \to \mathbb{R}$ be the D865: Standard natural real logarithm function.

Then \begin{equation} \frac{d \log(x)}{d x} = \frac{1}{x} \end{equation}

Proofs

Proof 0

Let $\log : (0, \infty) \to \mathbb{R}$ be the D865: Standard natural real logarithm function.

This result is a particular case of R4905: Derivative for standard natural real logarithm function. $\square$