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derivative of f(x) = x/(sqrt(x^2-4))

  • calc -

    I would rewrite it as
    y = x(x^2 - 4)^(-1/2_
    then use the product rule

    dy/dx = x(-1/2)(x^2-4)^(-3/2)(2x) + (x^2-4)^(-1/2)
    we could factor that

    dy/dx = (x^2-4)^(-3/2)[-x^2 + x^2-4]

    = -4/(x^2-4)^(3/2)

    check my work, I did not write it on paper first, did all the steps as I typed.

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