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Math Help - Derivative- quotient rule? Need help within hour if possible:)

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    Derivative- quotient rule? Need help within hour if possible:)

    Hi. I'm stuck on a problem I know is fairly simple, but I can not figure out what I am doing wrong.

    The problem is f'(x) of f(x)= (sqrt(x)-2)/(sqrt(x)+2)
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  2. #2
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    Quote Originally Posted by thedoge View Post
    Hi. I'm stuck on a problem I know is fairly simple, but I can not figure out what I am doing wrong.

    The problem is f'(x) of f(x)= (sqrt(x)-2)/(sqrt(x)+2)
    Hi,

    I've attached an image to show you what I've calculated.

    EB
    Attached Thumbnails Attached Thumbnails Derivative- quotient rule? Need help within hour if possible:)-ableitg_bild2.gif  
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  3. #3
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    Thanks mate! Cleared up my issue
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  4. #4
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    Quote Originally Posted by thedoge View Post
    Hi. I'm stuck on a problem I know is fairly simple, but I can not figure out what I am doing wrong.

    The problem is f'(x) of f(x)= (sqrt(x)-2)/(sqrt(x)+2)
    Now I don't normaly do the quotient rule as it is just a version of the
    product rule, but the quotient rule is:

    d/dx [g(x)/h(x)] = [h(x)g'(x) - g(x)h'(x)]/[g(x)]^2

    In your case g(x)=sqrt(x)-2, and h(x)=sqrt(x)+2, so:

    g'(x)=(1/2)/sqrt(x), and h'(x)=(1/2)/sqrt(x).

    Therefore applying the quotient rule:

    d/dx [sqrt(x)-2)/(sqrt(x)+2)]

    .........= [(sqrt(x)+2)/(2 sqrt(x)) - (sqrt(x)-2)/(2 sqrt(x))]/[sqrt(x)+2]^2

    Which simplifies to:

    d/dx [sqrt(x)-2)/(sqrt(x)+2)] = 2/(sqrt(x)[sqrt(x)+2]^2)

    RonL
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