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Implicit differentiation find dy/dx and d2y/dx2

  1. Oct 11, 2009 #1
    2xy=3x-y^2

    find dy/dx and d2y/dx2

    I just want to make sure my answer is right and simplified

    I got dy/dx= (3-2y)/ (2x+2y)

    Now d2y/dx2 took some time but this is what i got:

    (-12x+2x2y+9+4yx-14y-4y^2) / ((x+y)(2x+2y)^2)
     
  2. jcsd
  3. Oct 11, 2009 #2
    Your dy/dx is correct. I didn't work out the second derivative, but as long as you took the derivative of dy/dx using the quotient rule and implicit differentiation, replacing dy/dx in that expression with what you found, and then simplifying correctly, then you did it right.
     
  4. Oct 11, 2009 #3
    yeah, i did that must i just wasn't to sure with my algebra (thats usually the step i would mess up). thanks though!
     
  5. Oct 12, 2009 #4
    I dont know if you can reduce this to a more simpler form but this is simplest i got: y"=(3-2y)(3+8x+6y)/8(x+y)^3
     
  6. Oct 12, 2009 #5
    was this from the equation i have up there or did u do this from the begining of the problem?
     
  7. Oct 14, 2009 #6
    the answer is yes and yes.
     
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