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Seja f(x,y)=xy\sin(xy) , então \displaystyle \frac{\partial^2 f}{\partial...

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Seja $f(x,y)=xy\sin(xy)$ f(x,y)=xy\sin(xy), então

$\displaystyle \frac{\partial^2 f}{\partial y \partial x}(x,y)=$ \displaystyle \frac{\partial^2 f}{\partial y \partial x}(x,y)=

$-3xy\sin(xy)-(1-x^2y^2)\cos(xy)$ -3xy\sin(xy)-(1-x^2y^2)\cos(xy)

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$-xy\cos(xy)-x^2y\sin(xy)$ -xy\cos(xy)-x^2y\sin(xy)

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$-x^2y^2\sin(xy)-xy\cos(xy)+\sin(xy)$ -x^2y^2\sin(xy)-xy\cos(xy)+\sin(xy)

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$3xy\cos(xy)+(1-x^2y^2)\sin(xy)$ 3xy\cos(xy)+(1-x^2y^2)\sin(xy)

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