Natural Logarithm Function is Differentiable

Theorem
The natural logarithm function is differentiable and continuous.

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


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

From the corollary to the Fundamental Theorem of Calculus, $\ln$ is differentiable.

We also have that Differentiable Function is Continuous.

That was easy, wasn't it?