1. Not finding help here? Sign up for a free 30min 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!

Second derivative in terms of x and y?

  1. Dec 18, 2011 #1
    1. The problem statement, all variables and given/known data

    Find y" in terms of x and y:

    y^2 + 2y = 2x + 1

    2. Relevant equations

    N/A

    3. The attempt at a solution

    I found the first derivative:

    y^2 + 2y = 2x + 1
    2yy'+2y'=2
    2y'.(y+1)=2
    y'=2/2(y+1)
    y'=1/(y+1)

    But I'm having trouble moving on from there.
     
  2. jcsd
  3. Dec 18, 2011 #2

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Now, take the derivative of y'.

    Sure it will have y' in it, but then substitute the result you have for y' into that.
     
  4. Dec 18, 2011 #3
    alrighty so...

    y" = derivative of 1/y+1

    = (1)(y+1)^-1 ... then use product rule

    = 0 + (-1(y+1)^-2)y' ... then plug in y'

    = - [1/(y+1)]/(y+1)^2 ... combine

    y" = - 1/(y+1)^3 final answer


    ......

    I think I did it right. Does this satisfy "in terms of x and y?"
     
  5. Dec 18, 2011 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Looks good !
     
  6. Dec 18, 2011 #5
    thanks!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Second derivative in terms of x and y?
  1. Derivative y=√x+√x (Replies: 8)

Loading...