Question

What is the domain of the derivative of `ln x`?

Answer 1

The domain of the derivative of `lnx` is `(0, oo)`.

The domain of `f'` is a subsest of the domain of `f`.

Because the domain of `lnx` is `(0, oo)`, the domain of its derivative
which is defined to be: `lim_(hrarr0)(ln(x+h)-lnx)/h` cannot include any negative numbers.

Of course, we know that the derivative of `f(x) = ln(x)` is `f'(x) = 1/x`, which, as the derivative of `ln` has domain `(0, oo)`.