In general, two different mathematical operations need not commute. Let f(x,y) be a complex valued function, taking in two real-valued inputs x and y. Then under what circumstances is the partial derivative of the complex conjugate of f with respect to x equal to the complex conjugate of the partial derivative of f with respect to x ? Any help would be greatly appreciated!
2026-04-25 19:35:12.1777145712
Derivative of complex conjugate
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Only if $f$ is constant (in every connected component of its domain).
If $f$ is not constant, then $f(z)$ and $\overline{f(z)}$ cannot both have a derivative in the first place.