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Check my answer for implicit function problem?

  1. May 7, 2013 #1
    1. The problem statement, all variables and given/known data
    Use the IMPLICIT FUNCTION THEOREM (and not implicit differentiation) to find dy/dx at the point (1,1) when
    y^5 + x^2*y^3 − y*e^(x^2) = 1.


    2. Relevant equations
    f(x,y)=0
    dy/dx = - [f(x)/f(y)] = -[d/dx(f(x,y) / d/dy(f(x,y)]


    3. The attempt at a solution
    solving for f(x,y), i brought the 1 to the left side so the equation equaled 0, i.e y^5 + x^2*y^3 − y*e^(x^2)-1=0

    then d/dx of the function I got 2xy^3 - 2xye^(x^2)
    d/dy = 5y^4 + 3x^2y^2 - e^(x^2)

    so dy/dx was just -[d/dx / d/dy] = -[2xy^3 - 2xye^(x^2) / 5y^4 + 3x^2y^2 - e^(x^2)]
    for the point (1,1) i just plugged in x and y into the above equation, and got 0.65 as my answer.
     
    Last edited: May 7, 2013
  2. jcsd
  3. May 7, 2013 #2
    I got:

    dy/dx = -1.41
     
  4. May 7, 2013 #3
    can you show your work? did you get the same equation for dy/dx as me? if i got mine wrong it was probably the ye^(x^2) part, since i was kinda confused how to work it. for d/dx, i got 2xye^(x^2), and for d/dy i got e^(x^2).
     
  5. May 7, 2013 #4
    sorry, my mistake, I also got

    dy/dx = 0,65
     
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