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Compute d/(dx){sin^-1((1)/(sqrt(x+1)))}...

Compute `d/(dx){sin^-1((1)/(sqrt(x+1)))}`

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Knowledge Check

  • d/(dx) (sin^(-1) x/a)

    A
    `1/(sqrt(a^2 - x^2))`
    B
    `a/(sqrt(a^2 - x^2))`
    C
    `1/(sqrt(x^2 - a^2))`
    D
    None of these

  • d/dx[sin^(-1)(cos x)] =

    A
    `-sin x`
    B
    -1
    C
    x
    D
    `π/2-x`

  • d/dx(e^(2sin^-1x)) =

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

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

    d/dx{sin^-1(e^x)} is equal to :

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

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