Mapping Diagram Visualizing Complex Derivative:Powers
Mapping Diagram Visualizing Complex Derivative for Powers
The Complex Derivative and the Differential
Suppose is a domain, , and . Definition: The derivative of at , denoted , is defined by provided the limit exists. If exists for all in some open set containing , is called holomorphic at . Definition: Suppose is holomorphic at . The differential of at for , denoted , is defined by . Fact: If is holomorphic at and , then .