A) 1
B) -1
C) 0
D) 2
Correct Answer: C
Solution :
\[\because \] \[y={{\sin }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{x}{2}\] \[\therefore \] \[y=\frac{\pi }{2}\] \[\Rightarrow \] \[\frac{dy}{dx}=0\] Alternate Method: \[y={{\sin }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{x}{2}\] \[\frac{dy}{dx}=\left( \frac{2\left( \frac{1}{2} \right)}{\sqrt{4-{{x}^{2}}}} \right)+\left( \frac{-2\left( \frac{1}{2} \right)}{\sqrt{4-{{x}^{2}}}} \right)\] \[=\frac{1}{\sqrt{4-{{x}^{2}}}}-\frac{1}{\sqrt{4-{{x}^{2}}}}=0\]
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