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Differentiation of Quotients and Higher Derivatives

  1. Sep 19, 2014 #1
    1) The line 2x+9=3 meets curve xy+y+2=0 at the points P and Q. Calculate the gradient of the curve at P and Q

    2)Given that [itex]y=(x^2)/(x-2)[/itex], find
    a) [itex](d^2)y/dx^2[/itex] in its simplest form
    b)ther range of value for which [itex]dy/dx[/itex] and [itex](d^2)y/dx^2[/itex] are positive.


    I can't figure out either of the sums. For the first one I got the answer -1/11 & -44/81 (even though the answer page showed 1/2 and 4/81) and the second I couldn't do. Can anyone do them step by step?
     
  2. jcsd
  3. Sep 19, 2014 #2

    ehild

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    What is the first derivative of ##y=\frac{x^2}{x-2}##

    ehild
     
  4. Sep 19, 2014 #3
    y=(x^2)-4x/(x-2)^2
     
  5. Sep 19, 2014 #4

    Ray Vickson

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    How did you get
    [tex] \frac{d}{dx} \frac{x^2}{x-2} = x^2 - \frac{4x}{(x-1)^2} ? [/tex]
    This is obviously wrong.
     
  6. Sep 19, 2014 #5
    No, i got [itex]y= \frac{x^2-4x}{(x-2)^2} [/itex]
     
  7. Sep 19, 2014 #6

    HallsofIvy

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    Do you mean "2x+ 9y= 3"? What are P and Q?

    As Ray Vickson pointed out, you have written the first derivative incorrectly- although you may have calculated it correctly. You have the parentheses in the wrong place and you have the denominator wrong.
     
  8. Sep 19, 2014 #7
    Sorry for that, I suck at typing equations on computer.
     
  9. Sep 19, 2014 #8

    Mark44

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  10. Sep 19, 2014 #9

    ehild

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    Did you mean ##\frac{dy}{dx}##?


    ehild
     
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