# GATE2015-14

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 ?

1. $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial u}{\partial y}$
2. $\frac{df}{dz}=\frac{\partial u }{\partial x}+i\frac{\partial \nu }{\partial x}$
3. $\frac{df}{dz}=\frac{\partial \nu }{\partial y}-i\frac{\partial u }{\partial y}$
4. $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial \nu }{\partial x}$
in Others
edited