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Math Help - one more derivative -using quotient

  1. #1
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    one more derivative -using quotient

    find the derivative of

    x^2
    -----------
    root (x+1)

    the answer is

    x(3x+4)
    -------------
    2(x+1)^3/2

    using quotient rule, i got as far as:
    (2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
    --------------------------------------------
    x+1

    not quite sure what to do after...do i factor out?
    Thanks!
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  2. #2
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    Multiply and divide 2(x+1)^1/2 to the numerator and the denominator and simplify.
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  3. #3
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    Quote Originally Posted by calculus0 View Post
    find the derivative of

    x^2
    -----------
    root (x+1)

    the answer is

    x(3x+4)
    -------------
    2(x+1)^3/2

    using quotient rule, i got as far as:
    (2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
    --------------------------------------------
    x+1

    not quite sure what to do after...do i factor out?
    Thanks!
    [tex]Here you have y = \frac{u}{v}

    so \frac{dy}{dx} = \frac{v\,\frac{du}{dx} - u\,\frac{dv}{dx}}{v^2}.

    Which part are you having trouble with?
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  4. #4
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    so if i multiply top and bottom do i get:

    4x(x+1)3/2 - x^2
    ------------------------
    2(x+1)^2

    ? something is still wrong.. i think im getting closer, but still not the final answer
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  5. #5
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    Quote Originally Posted by calculus0 View Post
    find the derivative of

    x^2
    -----------
    root (x+1)

    the answer is

    x(3x+4)
    -------------
    2(x+1)^3/2

    using quotient rule, i got as far as:
    (2x)(x+1)^1/2 - (x^2)1/2(x+1)^1/2
    --------------------------------------------
    x+1
    That second term should be (x^2)(1/2)(x+1)^-1/2

    not quite sure what to do after...do i factor out?
    Thanks!
    You might find it easier to write this as x^2(x+1)^(-1/2) and use the product rule.
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  6. #6
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    Quote Originally Posted by calculus0 View Post
    so if i multiply top and bottom do i get:

    4x(x+1)3/2 - x^2
    ------------------------
    2(x+1)^2

    ? something is still wrong.. i think im getting closer, but still not the final answer
    (x+1)^1/2*(x+1)^1/2 = .............?

    (x+1)*(x+1)^1/2 = ...........?
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