I have $$F(z) = \phi + i\psi$$
Also, it is given that $$u = \frac{\delta \phi}{\delta x}, \ \ v = \frac{\delta\phi}{\delta y}$$ and $$u = \frac{\delta \psi}{\delta x}, \ \ v = -\frac{\delta\psi}{\delta y}$$
Now I have to prove that $$\frac{dF}{dz} = u - iv$$
But I am getting terms like $\dfrac{dx}{dz}$ and $\dfrac{dy}{dz}$ in the differentiated term. How do I proceed?
EDIT:
As pointed out the function $\psi$ was wrongly defined by me. It's actually
$$u = \frac{\delta \psi}{\delta y}, \ \ v = -\frac{\delta\psi}{\delta x}$$