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Math Help - how to find derivation of the following function

  1. #1
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    how to find derivation of the following function

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

    f(z) = e^{x^{2}+ y^{2}}[cos(2xy) + i sin(2xy)]
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  2. #2
    MHF Contributor

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    Re: 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
    \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
    u(x,y)= e^{x^2+ y^2}cos(2xy)
    v(x,y)= e^{x^2+ y^2}sin(2xy)
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