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f-x-y-x-x-2y-1-condition-on-x-and-y-to-have-f-symetric-2-find-f-x-f-y-2-f-x-y-2-f-y-x-3-find-2-f-2-x-and-2-f-2-y-




Question Number 146085 by mathmax by abdo last updated on 10/Jul/21
f(x,y)=x−(√(x+2y))  1)condition on x and y to have f symetric  2) find (∂f/∂x) ,(∂f/∂y) ,(∂^2 f/(∂x∂y)) ,(∂^2 f/(∂y∂x))  3) find (∂^2 f/∂^2 x) and (∂^2 f/∂^2 y)
$$\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{x}−\sqrt{\mathrm{x}+\mathrm{2y}} \\ $$$$\left.\mathrm{1}\right)\mathrm{condition}\:\mathrm{on}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:\mathrm{to}\:\mathrm{have}\:\mathrm{f}\:\mathrm{symetric} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{find}\:\frac{\partial\mathrm{f}}{\partial\mathrm{x}}\:,\frac{\partial\mathrm{f}}{\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{x}\partial\mathrm{y}}\:,\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{y}\partial\mathrm{x}} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{find}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{x}}\:\mathrm{and}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial^{\mathrm{2}} \mathrm{y}} \\ $$
Commented by mathmax by abdo last updated on 10/Jul/21
3)(∂^2 f/∂x^2 ) and (∂^2 f/∂y^2 )
$$\left.\mathrm{3}\right)\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{x}^{\mathrm{2}} }\:\mathrm{and}\:\frac{\partial^{\mathrm{2}} \mathrm{f}}{\partial\mathrm{y}^{\mathrm{2}} } \\ $$

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