Natural Logarithm Function is Differentiable/Proof 1

Theorem
The natural logarithm function is differentiable.

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


 * $\ln x = \displaystyle \int_1^x \frac 1 t \ \mathrm dt$

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