ComplexD[expr, aVariable]

Aliases: None

Description: $ComplexD[expr, aVariable]$ calculates the derivative of the complex expression $expr$ with respect to the ``complex'' variable $aVariable$. You can also calculate the derivative with respect to $Conjugate[aVariable]$. Try these examples:

$ComplexD[Conjugate[Exp[z + 1/Conjugate[z]]^2],z]$;
$ComplexD[Re[(1 + z w)^2]^2,w]$;
$ComplexD[Abs[1/(e^2 - 1) -z]^2,z]$;
$ComplexD[Conjugate[Exp[z + 1/Conjugate[z]]^2], Conjugate[z]]$;

Here is a second order derivative:

$ComplexD[Conjugate[Exp[z + 1/Conjugate[z]]^2, {z,2}]$;

Arguments: $expr$ is a complex expression. $aVariable$ is the variable in which to take the derivative with respect to.

Comments / Limitations: This only works for expressions defined with the commutative multiplication.