= Complex derivative
{title2=$f'(z)=\lim_{h\to0}(f(z+h)-f(z))/h$}
The complex derivative exists when this <limit> has the same finite value for increments $h$ approaching zero from every complex direction. For $f=u+iv$, real and imaginary increments give the necessary <Cauchy-Riemann equations>. Existence of those <partial derivatives> at one point alone is not sufficient for <complex differentiability at a point>; continuous <partial derivatives> in a neighbourhood, together with the <Cauchy-Riemann equations> there, give a standard sufficient condition for $f$ to be a <holomorphic function>.
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