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Math Help - Derivatives of a square

  1. #1
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    Derivatives of a square

    i have here (sq root of s)-1/(sq root of s)+1 how do i find the derivative of this??? i've been getting all these weird 1/2s and what not and cant figure out what im doing wrong
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  2. #2
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    Quote Originally Posted by cyberdx16 View Post
    i have here (sq root of s)-1/(sq root of s)+1 how do i find the derivative of this??? i've been getting all these weird 1/2s and what not and cant figure out what im doing wrong
    Lets assume that your function is:

    h(s)=(sqrt(s)-1)/(sqrt(s)+1).

    Now you probably need to use the quotient rule here, but I don't
    know the quotient rule so I will use the product rule:

    d/ds[f(s)/g(s)]=[df/ds]/g(s)-f(s)[dg/ds]/(g(s))^2.

    In this case f(s)=sqrt(s)-1, so df/ds=1/(2 sqrt(s)), and g(s)=sqrt(s)+1,
    so dg/ds=1/(2 sqrt(s), so we have:

    dh/ds=1/[2 sqrt(s) (sqrt(s)+1)] - (sqrt(s)-1)/[2 sqrt(s) (sqrt(s)+1)^2]

    which simplifies down to:

    dh/ds=1/[sqrt(s) (sqrt(s)+1)^2]

    (which is much easier to see if you write it out on paper (or if the
    mathematical type setting system we used to have here was working)

    RonL
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