A) \[\frac{2x{{e}^{y-x}}+2y(x+1)}{x(x{{e}^{y-x}}+2)}\]
B) \[\frac{2x{{e}^{x-y}}+2y(x+1)}{x(x{{e}^{y-x}}+2)}\]
C) \[-\frac{2x{{e}^{y-x}}+2y(x+1)}{x(x{{e}^{y-x}}+2)}\]
D) None of these
Correct Answer: C
Solution :
\[\frac{dy}{dx}=-\frac{\partial f/\partial x}{\partial f/\partial y}=-\frac{2x{{e}^{y}}+2xy{{e}^{x}}+2y{{e}^{x}}}{{{x}^{2}}{{e}^{y}}+2x{{e}^{x}}}\] \[=-\frac{2x{{e}^{y-x}}+2y(x+1)}{x(x{{e}^{y-x}}+2)}\], [Dividing \[{{N}^{r}}\]and\[{{D}^{r}}\]by \[{{e}^{x}}\]].
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