A) \[\frac{1}{1+{{x}^{2}}}-\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{-1}{1+{{x}^{2}}}-\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
C) \[\frac{1}{1+{{x}^{2}}}+\frac{{{a}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
D) None of these
Correct Answer: D
Solution :
\[\frac{d}{dx}{{\tan }^{-1}}\left( \frac{ax-b}{bx+a} \right)=\frac{1}{1+{{\left( \frac{ax-b}{bx+a} \right)}^{2}}}.\]\[\frac{d}{dx}\left( \frac{ax-b}{bx+a} \right)\] \[=\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}+{{a}^{2}}{{x}^{2}}+{{b}^{2}}{{x}^{2}}}=\frac{1}{1+{{x}^{2}}}\].
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