We have studied functions that take real inputs and give complex outputs (e.g., complex solutions to the damped harmonic oscillator, which are complex functions of time). For such functions, the deriv...We have studied functions that take real inputs and give complex outputs (e.g., complex solutions to the damped harmonic oscillator, which are complex functions of time). For such functions, the derivative with respect to its real input is much like the derivative of a real function of real inputs. It is equivalent to taking the derivatives of the real and imaginary parts, separately.
