Can someone, by any chance, have look at this
math.stackexchange.com/a/102888/59219 ? In particular, why does this equation $ \lim\limits_{h\to 0}\frac{\overline{f(\overline{z+h})}-\overline{f(\overline z)}}{h} =\lim\limits_{h\to 0}\overline{\left( \frac{f(\overline z+\overline h)-f(\overline z)}{\overline h} \right)} $ hold?