Natural Logarithm Function is Differentiable/Proof 1

Theorem

The (real) natural logarithm function is differentiable.

Proof

This proof assumes the definition of $\ln$ as:

$\ln x = \ds \int_1^x \frac 1 t \rd t$

As $\ln$ is defined as a definite integral, the result follows from the corollary to the first fundamental theorem of calculus.

$\blacksquare$