Or, can we differentiate holomorphic functions only?
Wirtinger defined two derivations in complex analysis for which we have: diff(x,conjugate(x)) = 0 and diff(conjugate(x),x) = 0.
http://en.wikipedia.org/wiki/Wirtinger_derivatives
Wirtinger calculus has important applications in optimization and has been extended to quaternion functions.
Is there any situation in which leaving diff(conjugate(x),x) unevaluated is an advantage?
