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Question

The differential coefficient of the function tan12x1x2 w.r.t. x2 is-

A
11+x2
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B
11x2
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C
1x(1+x2)
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D
x1+x2
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Solution

The correct option is C 1x(1+x2)
ddx(tan12x1x2)=ddx(2x1x2)1+(2x1x2)2
=(1x2)(2)(2x)(2x)(1x2)21+(2x1x2)2=22x2+4x2(1x2)2+(2x)2
=2x2+21+x42x2+4x2=2(x2+1)(x2+1)=2x2+1

ddx(x2)=2x

Therefore derivative of tan1(2x1x2) w.r.t x2 is
=2x2+1×12x=1x(x2+1)

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