A) \[\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]
B) \[\pi \]
C) \[0\]
D) \[1\]
E) \[\frac{1}{x\sqrt{{{x}^{2}}-1}}\]
Correct Answer: C
Solution :
Given that, \[y={{\tan }^{-1}}x+{{\sec }^{-1}}x+{{\cot }^{-1}}x+\cos e{{c}^{-1}}x\] Differentiating it w.r.t.\[x,\]we get \[\frac{dy}{dx}=\frac{1}{1+{{x}^{2}}}+\frac{1}{x\sqrt{{{x}^{2}}-1}}-\frac{1}{1+{{x}^{2}}}-\frac{1}{x\sqrt{{{x}^{2}}-1}}\] \[=0\]
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