1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

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

  4. Sep 19, 2014 #3
  5. Sep 19, 2014 #4

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Science Advisor

    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


    Staff: Mentor

  10. Sep 19, 2014 #9


    User Avatar
    Homework Helper

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

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted