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Math Help - Quotient Rule - Factorization Question

  1. #1
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    Quotient Rule - Factorization Question

    Hi, I am not sure how the 1/2x^-1/2 was factorized out in this numerator that was derived from the quotient rule. Can some please explain.

    = (x^2 + 1) (1/2x^-1/2) x^1/2 (2x)
    =1/2x^-1/2 (x^2 +1 4x^2)
    I understand how factorization works but I am not sure what happened in this case.

    Thank you.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    =1/2x^-1/2 (x^2 +1 4x^2)
    isn't correct

    recall x^(1/2) = x^(-1/2) * x


    (1/2x^-1/2) x^1/2 (2x) = x^(-1/2)[ 1/2 -x (2x)]

    = 1/2x^(-1/2)[1-4x^2]
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