A derivative of a complex function, which must satisfy the Cauchy-Riemann equations in order to be complex differentiable.

Krantz, S. G. "The Complex Derivative." §1.3.5 and 2.2.3 in Handbook of Complex Variables. Boston, MA: Birkhäuser, pp. 15-16 and 24, 1999.

CITE THIS AS:

Weisstein, Eric W. "Complex Derivative." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/ComplexDerivative.html