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    If I have functions f(u,v) and u=x^2+y^2 and v=x^2-y^2, how do i express the second order partial derivative with respect to x in terms of derivatives of f with respect to u and v?
    EDIT: nvm I got it.

    Typing it all out in latex would take forever. here is a good start:

    f_u = \frac{ \partial f}{ \partial u}
    f_v = \frac{ \partial f}{ \partial v}
    u_x = \frac{ \partial u}{ \partial x}
    v_x = \frac{ \partial v}{ \partial x}

    \displaystyle \frac{ \partial }{ \partial x} ( \frac{ \partial f(u,v)}{ \partial x})= \frac{ \partial }{ \partial u}(f_u u_x +f_v v_x) u_x + \frac{ \partial }{ \partial v}(f_u u_x +f_v v_x) v_x

    you have to expand this writing, you have to write u_x and v_x as functions of u & v
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Updated: April 4, 2011
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