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Implicit diffrantiation

  1. Nov 22, 2007 #1
    1. The problem statement, all variables and given/known data

    I need to find a tangent line equation but my main problem is isolating actually.

    sqrt ( 2x + 2y ) + sqrt ( 3xy) = 13





    3. The attempt at a solution

    0.5 ( 2x + 2y ) ^ -0.5 (2+2y') + 0.5(3xy) ^ -0.5 ( 3 ( y + y' x ) ) = 0

    this is where I get stuck
     
  2. jcsd
  3. Nov 23, 2007 #2
    The differentiation looks good to me. Now you just need to simplify.

    If you're having trouble, I'd multiply out
    0.5 ( 2x + 2y ) ^ -0.5 (2+2y')

    and
    0.5(3xy) ^ -0.5 ( 3 ( y + y' x ) )

    and then pull a y' out of two terms, move the remaining terms to the other side and divide by what's multiplied with y'.
     
  4. Nov 23, 2007 #3

    HallsofIvy

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    Don't let the fact that it looks complicated stop you. The equation you get by "implicit differentiation" is always linear in y'. Separating y' as Martin III said should be easy.

    0.5(2x+2y)1/2(2x+ 2y')+ 0.5(3xy)1/2(3y+ 3y')= 0
    (2x+2y)1/2x+ (2x+2y)1/2y'+ (3/2)y(3xy)1/2+(3/2)y'(3xy)1/2= 0
    [(2x+2y)1/2+ (3/2)(3xy)1/2]y'= -(2x+2y)1/2x- (3/2)y(3xy)1/2.

    In fact, since you say you are to "find a tangent line equation", you must be given some point at which to find the tangent line. If you just put the values you are given for x and y into the original equation you should find it much easier.
     
    Last edited: Nov 23, 2007
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