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f-R-2-R-f-x-f-y-f-x-y-




Question Number 2172 by 123456 last updated on 06/Nov/15
f:R^2 →R  (∂f/∂x)=(∂f/∂y)  f(x,y)=??
$${f}:\mathbb{R}^{\mathrm{2}} \rightarrow\mathbb{R} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial{f}}{\partial{y}} \\ $$$${f}\left({x},{y}\right)=?? \\ $$
Answered by prakash jain last updated on 06/Nov/15
f(x)=ce^(x+y)   (∂f/∂x)=(∂f/∂y)=ce^(x+y)
$${f}\left({x}\right)={ce}^{{x}+{y}} \\ $$$$\frac{\partial{f}}{\partial{x}}=\frac{\partial{f}}{\partial{y}}={ce}^{{x}+{y}} \\ $$

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