Natural logarithm/Derivative/Fact

Derivative of natural logarithm

The derivative of the natural logarithm

$\ln \colon \mathbb {R} _{+}\longrightarrow \mathbb {R} ,x\longmapsto \ln x,$

is

$\ln \!'\colon \mathbb {R} _{+}\longrightarrow \mathbb {R} ,x\longmapsto {\frac {1}{x}}.$

Proof, Write another proof