What is the meaning of $\partial_{x}$ in this question?

Question

I don't want to know how to solve this question. Rather, I would like to know what the $\partial_{x}$ means. Here is the question:

Prove that if $f(z)$ is differentiable at a point $z_{0} \in \Omega$, then $f′(z_{0}) = \partial_{x} f(z_{0})$.

I was thinking maybe that since $z$ can be expressed as $x+iy$ then $\partial_{x} f(z_{0})$ would be the derivative of the function on the real part, but I'm not sure.

Answer 1

$f(z)$ is a function, and is differentiable at a point called $z_0$ in some set $\Omega$.

Then, it says that $f'(z_0)=\partial_x f(z_0)$

So like, $f'(z_0)=\dfrac{d(f(z_0))}{dx}$

Answer 2

I want to add something here it is stated that if the differentiation exists then it is same as the directional derivative at any direction. Now the direction $e_1=(1,0)$ has been chosen, which is $\partial_x:= \frac{\partial}{\partial_x}$ in particular.