A complex-valued function, $f(z)$, given below is analytic in domain $D$:
$$f\left ( z \right )=u\left ( x,y\right )+i\nu \left ( x,y\right )\:\:\:\:\:\:\:z=x+iy$$
Which of the following is $NOT$ correct ?
- $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial u}{\partial y}$
- $\frac{df}{dz}=\frac{\partial u }{\partial x}+i\frac{\partial \nu }{\partial x}$
- $\frac{df}{dz}=\frac{\partial \nu }{\partial y}-i\frac{\partial u }{\partial y}$
- $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial \nu }{\partial x}$