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Math Help - Find partial derivative...

  1. #1
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    Find partial derivative...

    Find the partial derivatives of  F(x,y) = f( g(x) k(y), h(x) + 2k(y) ) .

    Partial derivatives are easy for me when the function is written g(x,y) = x^2 - sin(y) or something like that, but when it's written as a composition of functions, I start to get confused. Could someone please help me with this?
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  2. #2
    Member Mauritzvdworm's Avatar
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    just use the chain rule and we make the following definitions

    p(x,y):=g(x)k(y)
    q(x,y):=g(x)+2k(y)

    \frac{\partial F}{\partial x}=\frac{\partial f}{\partial p}\frac{\partial p}{\partial g}\frac{\partial g}{\partial x}+\frac{\partial f}{\partial q}\frac{\partial q}{\partial g}\frac{\partial g}{\partial x}

    and similarly for y, remembering that y is in the functions k
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