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Question

If y=tan1x1x2x+1x2, then dydx is equal to.

A
11x2
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B
11x2
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C
x1x2
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D
None of these
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Solution

The correct option is B 11x2
Formula:
tan1(tanx)=x

Let, x=cosθθ=cos1x

y=tan1(x1x2x+1x2)

y=tan1(cosθ1cos2θcosθ+1cos2θ)

y=tan1(cosθsinθcosθ+sinθ)

y=tan1(1tanθ1+tanθ)

y=tan1[tan(π4θ)]

y=π4θ

y=π4cos1x

dydx=011x2

dydx=11x2

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