calculus quick question

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g(x)= sqrt(1-4x^2)

Can someone help me find the first and second derivatives please!

  • calculus quick question -

    write it as

    g(x) = (1 - 4x^2)^(1/2)
    g ' (x) = (1/2)(1 - 4x^2)^(-1/2) (-8x)
    = -4x(1 - 4x^2)^(-1/2)

    now by the product rule

    g '' (x)
    = (-4x)(-1/2)(1-4x^2)^(-3/2) (-8x)- 4(1 - 4x^2)^(-1/2)
    = (-16x^2)(1-4x^2)^(-3/2) - 4(1 - 4x^2)^(-1/2)
    = -4(1 - 4x^2)^(-3/2) [ 4x^2 - (1-4x^2) ]
    = -4(1-4x^2)^(-3/2) (4x^2 + x - 2)
    = -4( 1-4x^2)^(-3/2)
    = -4/(1 - 4x^2)^(3/2)

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