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Homework Help: Did i find the derivative correctly?

  1. May 7, 2006 #1
    Hi there,
    Just wondering if i found dy/dx of (x+1)^2/1+x^2 = 2(x+1)/2x and also the second derivative d^2 y/dx^2=(x+1)/2
    Is that correct?? I don't think it is.
  2. jcsd
  3. May 7, 2006 #2
    No its not the derivative of a quotient is not equal to the quotient of the derivatives. Have you learned the quotient rule for differentiating these kinds of functions?
  4. May 7, 2006 #3
    Aww i have to use the quotient rule?? *sigh*
    Well we didn't go that far:( More work! Thanks anyway!
  5. May 7, 2006 #4


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    Homework Helper

    Well, you don't *have* to. You can use one of multiple methods,

    for example, partial fraction decomposition into elementary functions with complex factors in the denominator.

    Or even substitute [tex]x = tan \theta[/tex] simplify with trig identities first, then observe that [tex]\frac{dy}{dx} = \frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}[/tex]

    There are many way to skin a cat. :wink:
  6. May 8, 2006 #5


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    Gold Member

    Have you learned the product rule? The quotient rule is just a special case of the product rule.

    Your function is a product of [tex](x+1)^2[/tex] and [tex](1+x^2)^{-1}[/tex]
    Last edited: May 8, 2006
  7. May 8, 2006 #6
    Yeah we've learnt the product rule, chain and all....just that we have to graph that, but doing it without a graphics calculator.
    I think i get it now.
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