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B
2x(x2+2)2
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C
x2+1x2+2
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D
None
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Solution
The correct option is B2x(x2+2)2 y=cos2[tan−1(sin(cot−1x))]cot−1x=zx=cotzsinz=1√1+x2z=sin−11√1+x2 z=sin−11√1+x2y=cos2[tan−1(sin(sin−11√1+x2))] =cos2[tan−11√1+x2]Lettan−11√1+x2=utanu=1√1+x2y=cos2(cos−1√1+x22+x2)y=cos2(coscos−1√1+x22+x2)(coscos−1√1+x22+x2)y=1+x22+x2dydx=(2+x2)(2x)−(1+x2)(2x)(2+x2)2=4x+2x3−2x−2x3(2+x2)2=2x(2+x2)2.