Derivative

Let $D$ be a subset of complex numbers, $z_0 \in D$, and let $f \colon D \rightarrow \mathbb{C}$ be a function. We say that $f$ is (complex-) differentiable at $z_0$ if the limit $$f'(z_0)=\displaystyle\lim_{h \rightarrow 0} \dfrac{f(z_0+h)-f(z_0)}{h}$$ exists.

Properties

Derivative is a linear operator
Relationship between q-derivative and derivative