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Find y'' by implicit differentiation

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data

    Find y'' by implicit differentiation.

    2. Relevant equations

    _LARGE_9x2y29.gif

    3. The attempt at a solution

    _LARGE__fracddx9x2y2_fracddx9.gif

    _LARGE_18x2y_fracddx0.gif

    _LARGE_2y_fracddx-18x.gif

    _LARGE__fracddx_frac-18x2y.gif

    _LARGE__fracddx_frac-9xy.gif

    I get to this point in the problem, which is I solved for y'. But then when I attempt to take y'', in other words take the derivative of my answer for y', I don't get the answer that is in the back of the book.

    Many thanks in advance,
    Bob
     

    Attached Files:

  2. jcsd
  3. Oct 11, 2009 #2

    Mark44

    Staff: Mentor

    You went astray in the 2nd line and all following lines. The second line should be
    18x + 2y dy/dx = 0 and your last line should be dy/dx = -9x/y. Now take the derivative again, keeping in mind that you need to use the quotient rule and the chain rule, in that order.
     
  4. Oct 11, 2009 #3

    rock.freak667

    User Avatar
    Homework Helper

    so y*y'=-9x

    so take d/dx of both sides

    for d/dx(y*y') use the product rule .
     
  5. Oct 12, 2009 #4
    Bob, your last equation can be rewritten as; y'=-9xy^-1---->from here here you may get the y" by product rule and arrive at having y"=9/y^2(x-y)--->is this what you got in your book?
     
  6. Oct 12, 2009 #5
    You can rewrite your last equation to: yy'=-9x---> from here try implicit differentiation.
    You'll arrive at having: yy"+y'y'=-9; next, substitute the value of y'=-9x/y (previously derived); You'll arrive at having: y"=-9/y^3(9x^2+y^2).
     
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