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Math Help - Derivative Question Problems

  1. #1
    s3a
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    Derivative Question Problems

    Can someone please give me the full detailed solutions for both problems? The questions are to find the derivative functions of these functions (using the quotient rule).

    Problem 1:

    y = (r^2)/(1 + sqrt(r))

    Problem 2:

    f(x) = x/(c + c/x)

    Answer (1): y' = r(4 + 3sqrt(r))/2(1 + sqrt(r))^2
    Answer (2): y' = 2cx/(x^2 + c)^2

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
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    Quote Originally Posted by s3a View Post
    Can someone please give me the full detailed solutions for both problems? The questions are to find the derivative functions of these functions (using the quotient rule).

    Problem 1:

    y = (r^2)/(1 + sqrt(r))

    Problem 2:

    f(x) = x/(c + c/x)

    Answer (1): y' = r(4 + 3sqrt(r))/2(1 + sqrt(r))^2
    Answer (2): y' = 2cx/(x^2 + c)^2

    Any help would be greatly appreciated!
    Thanks in advance!
    y = \frac{r^2}{1+\sqrt{r}}

    y' = \frac{(1+\sqrt{r})(2r) - (r^2)\left(\frac{1}{2\sqrt{r}}\right)}{(1+\sqrt{r}  )^2}

    you clean up the algebra


    for the second one, start by multiplying numerator and denominator by x to clear the fraction in the denominator ...

    f(x) = \frac{x^2}{cx + c}

    now use the quotient rule.
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  3. #3
    s3a
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    I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.
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  4. #4
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    Quote Originally Posted by s3a View Post
    I got those steps right so that's not my problem. [snip]
    Then how about you show all your workoing so that we can see what is your problem. Or just use this website: http://www.wolframalpha.com/.
    Quote Originally Posted by s3a View Post
    [snip]By the way, you didn't add the primes on y' = derivative_function.
    Tsk tsk skeeter. Your pay will be docked this week. (Sheesh, that's the thanks you get ....).
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  5. #5
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    Quote Originally Posted by s3a View Post
    I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.
    huh?
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  6. #6
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    Quote Originally Posted by s3a View Post
    I got those steps right so that's not my problem. By the way, you didn't add the primes on y' = derivative_function.
    There is no indication that he went back and editted after you wrote this and I certainly see a ' on his derivative!
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  7. #7
    s3a
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    I guess I came off as rude, I obviously didn't mean that. But with the y' = derivative_function, I meant the stuff after the y' = has 2 " ' " signs missing. My work is attached as a pdf file. (#17, #25)
    Attached Files Attached Files
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  8. #8
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    Quote Originally Posted by s3a View Post
    I guess I came off as rude, I obviously didn't mean that. But with the y' = derivative_function, I meant the stuff after the y' = has 2 " ' " signs missing. My work is attached as a pdf file. (#17, #25)
    did it ever occur to you that those 'prime' signs are not necessary?

    note that 2r = (r^2)'
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  9. #9
    s3a
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    Oh yes you're right, I skimmed through it but my teacher basically explained both to me in person so I get them but thanks for the effort and sorry if I offended you or something.
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