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