is called the derivative of at . The rules for
differentiation in real functions can also be applied to complex functions. So,
go through
Differentiability — Real Analysis.
Singular point
If is not differentiable at then is called a singular point
of .
Neighbourhood
Suppose . A neighborhood of is the region contained in
the circle .
Analytic
A function is said to be analytic at iff it is differentiable
throughout a neighbourhood of .