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Let y = arcsin x, x is an element of ]-1, 1[. Show that d^2y/dx^2 = 2-x^2/(1-x^2)^3/2

  • math -

    straightforward derivative. Where do you get stuck?

    y' = (1-x^2)^(-1/2)
    now just use the power rule and chain rule to get y"

  • math -

    Sorry i meant x arrsin x.

    So I thought the first derivative of that would be
    x/sqrt1-x^2 + arcsinx

  • math -

    xarcsinx*

  • math -

    I get stuck on the second derivative, trying to get it to equal 2-x^2/(1-x^2)^3/2.

    I think that from my first derivative, you have to sure the quotient rule

  • math -

    *use the quotient rule

  • math -

    I tried to use the quotient rule but I get stuck simplifying it.
    I got

    (sqrt1-x^2)(1/sqrt1-x^2) - (x+arcsinx)(1/2(1-x^2)2x) / (sqrt1-x^2)^2

  • math -

    please help me. I don't know what I am doing wrong

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