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Multiple Choice Questions

Find dy dx if y cos 1 x x 1 x x 1 ........

Mathematics (NDA) Diffrentiation
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    Find dy/dx ,if y=cos-1  (x-x-1  /x+x-1)?

     2/1-x2

    Incorrect Answer

     -2/1+x2

    Correct Answer

    -1/1+x2

    Incorrect Answer

    2/1+x2

    Incorrect Answer
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    Explanation:

    y=cos-1  (x-x-1  /x+x-1)

    = cos-1  (x2  -1  /x2  +1)

    X=tanθ

    Θ  =tan-1  x

    Y=  cos-1  (tan2 θ   -1/ tan2 θ   +1)

    = cos-1  (1-tan2 θ/ tan2 θ   +1)

    = cos-1  (-cos2θ)

    = cos-1  (cos π-2θ)

    =π -2θ

    =π- 2 tan-1 x

    dy/dx  = 0- 2/1+x2

    = -2/1+x2

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