A) \[\frac{{{e}^{x}}(1+x)}{{{(1+{{x}^{2}})}^{2}}}\]
B) \[\frac{{{e}^{x}}{{(1-x)}^{2}}}{{{(1+{{x}^{2}})}^{2}}}\]
C) \[\frac{{{e}^{x}}{{(1+x)}^{2}}}{(1+{{x}^{2}})}\]
D) \[\frac{{{e}^{x}}{{(1-x)}^{2}}}{(1+{{x}^{2}})}\]
Correct Answer: B
Solution :
\[\frac{d}{dx}\left( \frac{{{e}^{x}}}{1+{{x}^{2}}} \right)=\frac{(1+{{x}^{2}}){{e}^{x}}-{{e}^{x}}(2x)}{{{(1+{{x}^{2}})}^{2}}}=\frac{{{e}^{x}}{{(1-x)}^{2}}}{{{(1+{{x}^{2}})}^{2}}}\]
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