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Question

ddx{cos2[Tan1(sin cot1x)]}=

A
2(x2+2)2
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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 B 2x(x2+2)2

y=cos2[tan1(sin(cot1x))]cot1x=zx=cotzsinz=11+x2z=sin111+x2
z=sin111+x2y=cos2[tan1(sin(sin111+x2))]
=cos2[tan111+x2]Let tan111+x2=utanu=11+x2y=cos2(cos11+x22+x2)y=cos2(cos cos11+x22+x2)(cos cos11+x22+x2)y=1+x22+x2dydx=(2+x2)(2x)(1+x2)(2x)(2+x2)2=4x+2x32x2x3(2+x2)2=2x(2+x2)2.

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