A) \[(-\infty ,\,-1]\]
B) \[(-\infty ,\,0]\]
C) \[[1,\infty )\]
D) \[(0,\infty )\]
Correct Answer: D
Solution :
\[y=\frac{1}{1+{{x}^{2}}}\]Þ\[\frac{dy}{dx}=-\frac{2x}{{{(1+{{x}^{2}})}^{2}}}\] To be decreasing, \[-\frac{2x}{{{(1+{{x}^{2}})}^{2}}}<0\]Þ\[x>0\Rightarrow x\in (0,\infty )\].
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