Sometimes we need a good approximation to the derivative of a real-valued function at some real value . So here’s a fun fact that you may not know. If is a small positive number and can be evaluated at a complex argument, then where is the imaginary unit and denotes the imaginary part of a complex number. This unexpected but highly accurate approximation is called complex step differentiation . The method dates back to Lyness and Moler (1967) ; Squire and Trapp (1998) give a concise modern expos