complex partial differentiation?

[kakarukeys]

I know complex total differentiation is defined in analytic function theory.

df = f'(z) dz
z = x + iy, dz = dx + idy

Is there complex partial differentiation?

Given a real value function
F(z^*, z, t)

How would you define
\partial F\over\partial z
\partial F\over\partial z^*
?

[HallsofIvy]

If F is a function of two or three variables, define partial derivatives for complex numbers exactly like you do for real numbers. You do understand, do you not, that the derivative for complex numbers is defined in exactly the same way as for real numbers (except, of course, that all numbers are allowed to be complex)?