A) \[\frac{1}{1+25{{x}^{2}}}+\frac{2}{1+{{x}^{2}}}\]
B) \[\frac{5}{1+25{{x}^{2}}}+\frac{2}{1+{{x}^{2}}}\]
C) \[\frac{5}{1+25{{x}^{2}}}\]
D) \[\frac{1}{1+25{{x}^{2}}}\]
Correct Answer: C
Solution :
\[[-3,0]\] \[={{\tan }^{-1}}\frac{5x-x}{1+5x.x}+{{\tan }^{-1}}\frac{\frac{2}{3}+x}{1-\frac{2}{3}.x}\] \[=6x{{e}^{{{x}^{2}}}}-6x{{e}^{{{x}^{2}}}}+\frac{1}{3}(3)-0=1\] Þ \[\frac{dy}{dx}=\frac{5}{1+25{{x}^{2}}}\].
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