I am running into issues trying to find the derivation of f(z) below. Please help

$\displaystyle f(z) = e^{x^{2}+ y^{2}}[cos(2xy) + i sin(2xy)]$

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- Nov 1st 2012, 11:05 AMflametag2how to find derivation of the following function
I am running into issues trying to find the derivation of f(z) below. Please help

$\displaystyle f(z) = e^{x^{2}+ y^{2}}[cos(2xy) + i sin(2xy)]$ - Nov 1st 2012, 02:46 PMHallsofIvyRe: how to find derivation of the following function
Technically the word is "differentiation", not "derivation".

I presume you know that if f(z)= f(x+ iy)= u(x, y)+ iv(x,y) then

$\displaystyle \frac{df}{dz}= \frac{\partial u}{\partial x}+ i \frac{\partial v}{\partial y}= \frac{\partial v}{\partial y}- i\frac{\partial v}{\partial y}$

(The fact that those two expressions on the right are equal is the "Cauchy- Rieman" equations. You can use either one.)

Here, of course, you have

$\displaystyle u(x,y)= e^{x^2+ y^2}cos(2xy)$

$\displaystyle v(x,y)= e^{x^2+ y^2}sin(2xy)$