A) \[\frac{1}{1+{{x}^{2}}}\]
B) \[-\frac{1}{1+{{x}^{2}}}\]
C) \[\frac{2}{1+{{x}^{2}}}\]
D) \[-\frac{2}{1+{{x}^{2}}}\]
Correct Answer: B
Solution :
\[y={{\cot }^{-1}}\left( \frac{1+x}{1-x} \right)\] \[\frac{dy}{dx}=-\frac{1}{1+{{\left( \frac{1+x}{1-x} \right)}^{2}}}\left[ \frac{(1-x)+(1+x)}{{{(1-x)}^{2}}} \right]\] \[=-\frac{2{{(1-x)}^{2}}}{2(1+{{x}^{2}})(1-{{x}^{2}})}=-\frac{1}{1+{{x}^{2}}}\].You need to login to perform this action.
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