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: Implicit differentiation, find y''

  1. Sep 16, 2011 #1

    apiwowar

    User Avatar

    the problem is to find y'' or d2y / d2x

    the equation is y2 = x2

    first i found the first derivative dy/dx = 2x / 2y = x / y

    then i found the second using the quotient rule and got

    y'' = (y - x(dy/dx)) / y2

    i plugged in y' into y'' and got

    y'' = (y - (x2/y)) / y2

    but then im stuck after that because when i simplify i get
    y'' = (y2 - x2) / y3

    i dont know how i can plug the original equation back in.

    did i go wrong somewhere?
     
    apiwowar, Sep 16, 2011
  2. jcsd
    Phys.org - latest science and technology news stories on Phys.org
  3. Sep 16, 2011 #2

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    This looks fine.
    This looks fine, too.
    This above is correct, but can be simplified. If y2 = x2, then y2 - x2 = ?
     
    Mark44, Sep 16, 2011
  4. Sep 16, 2011 #3

    ehild

    User Avatar
    Homework Helper

    Take care, you have to exclude x=y=0.
    The original equation is y2=x2. What do you get when you plug that in?

    ehild
     
    ehild, Sep 16, 2011
  5. Sep 16, 2011 #4

    apiwowar

    User Avatar

    does x2-y2 = 0 or 1?

    and the book shows that the answer is 3y/4x2 = 3x / 4y, hows that possible? shouldnt the answer be y'' = ......?
     
    apiwowar, Sep 16, 2011
  6. Sep 16, 2011 #5

    Mark44

    User Avatar
    Insights Author

    Staff: Mentor

    If two numbers are equal, then subtracting one from the other leaves zero.
    Yes, they're asking you for y'', so the answer should start with y'' = ...

    I don't see how they got 3y/4x2 = 3x / 4y.

    Going back to the original problem, you have y2 = x2, which is equivalent to two equations: y = x or y = -x. For the first, y' = 1, and for the second, y' = -1. What do these tell you about y''?
     
    Mark44, Sep 16, 2011
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...
Similar Threads for Implicit differentiation find
2nd order differential equations
Continuous or differentiable
I need some help with implicit differentiaiton.
Implicit Euler ODE BC
Finding dy/dx for a circle