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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. $\frac{df}{dz}=\frac{\partial \nu }{\partial y}+i\frac{\partial \nu }{\partial x}$ 
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