Differentiable
A Function is said to be differentiable at a point if its Derivative exists at that point. Let 
and
on some region 
containing the point 
. If 
satisfies the Cauchy-RiemannEquations and has continuous first Partial Derivatives at , then 
exists and isgiven by
and the function is said to be Complex Differentiable. Amazingly, there exist ContinuousFunctions which are nowhere differentiable. Two examples are the Blancmange Function andWeierstraß Function.See also Blancmange Function, Cauchy-Riemann Equations, Complex Differentiable, Continuous Function,Derivative, Partial Derivative, Weierstraß Function
- Three
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