Show that the inverse function to $f(x)=\int_{1}^{x}\frac{dt}{t}$ is differentiable

Question

Show that the inverse function to $$f(x)=\int_{1}^{x}\frac{dt}{t}$$ is differentiable.

I know that the integral is $\ln(x)$, but I don't know how to show that it is differentiable in a good way

Thanks for help