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Math Help - Find derivative

  1. #1
    DBA
    DBA is offline
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    Find derivative

    Hi, I need to find the derivative and I do not know what I did wrong...

    y=4x/ sqt(x+1)

    --> y=4x * (x+1)^-1/2 then I used the

    Product Rule f(x)*g'(x) + g(x)*f'(x)

    f(x)=4x
    g(x)=(x=1)^-1/2


    y'= 4x * -1/2 * (x+1)^-3/2 + [(x+1)^-1/2] * 4

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

    = -2x / (x+1)^3/2 + 4 * (x+1) / [(x+1)^1/2] * (x+1)

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

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

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

    = 2(x+2) / (x+1)^3/2

    The solution shoud be y'= -x-4/ (x+1) ^5/2

    Can anyone let me knwo what I did wrong?
    Thanks!
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  2. #2
    DBA
    DBA is offline
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    Oh, I am sorry. I guess I just figured it out. In the solution they went on to find the second derivative - y''

    So
    y' = 2(x+2) / (x+1)^3/2
    and
    y'' = y'= -x-4/ (x+1) ^5/2
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