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The differential coefficient of tan^(- ...

The differential coefficient of `tan^(- 1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))`

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If y=tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))), find (dy)/(dx)

Differentiate (sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))

Knowledge Check

  • The derivative of tan^(-1)((sqrt(1 + x)-sqrt(1-x))/(sqrt(1 + x)+sqrt(1-x))) is

    A
    `sqrt(1 - x^(2))`
    B
    `(1)/(sqrt(1-x^(2)))`
    C
    `(1)/(2sqrt(1-x^(2)))`
    D
    x

  • d/(dx){Cot^(-1)""(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}

    A
    `1/(sqrt(1-x^2))`
    B
    `(-1)/(2(sqrt(1-x^2)))`
    C
    `(1)/(sqrt(1+x^2))`
    D
    `(-1)/(2(1+x^2))`

  • The derivative of tan^(-1) ((sqrt1+x-sqrt1-x)/(sqrt 1+x+ sqrt1-x)) is

    A
    `(sqrt1-x^2`
    B
    `1/(sqrt1-x^2`
    C
    `1/(2sqrt1-x^2`
    D
    x

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    Differentiate the function w.r.t. x, tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))) .

    Differentiate tan^(-1) ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) w.r.t. x .

    Differentiate tan^(-1) ((sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))) w.r.t.x.

    Differentiate the following with respect of x:tan^(-1)((sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x)))

    Differentiate tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))

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