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Implicit Differentiation w/ trig functions check

  1. Oct 15, 2008 #1
    1. The problem statement, all variables and given/known data
    Determine dy/dx when

    y*sin(x2)=5

    3. The attempt at a solution
    y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0

    2xy cos(x2)*dy/dx = -sin(x2)

    dy/dx = -sin(x2) / 2xy cos(x2)

    dy/dx = -2xy tan(x2)
     
  2. jcsd
  3. Oct 15, 2008 #2

    Dick

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    How did 2xy magically pop from the denominator to the numerator?
     
  4. Oct 15, 2008 #3
    Would it be +2xy tan(x2)?
     
  5. Oct 15, 2008 #4
    y*2xcos(x2) dx/dx + sin(x2)*1 dy/dx = 0

    2xy cos(x2)*dy/dx = -sin(x2)

    What I notice is that you separated sin(x^2)dy/dx by subtraction..which is obviously "illegal"

    Try isolating the term with dy/dx in it and then try to isolate just the dy/dx
     
  6. Oct 15, 2008 #5
    I didn't even notice I did that :yuck:

    Working it out again:

    y*2xcos(x2) dx/dx + sin(x2)dy/dx = 0

    sin(x2)dy/dx = -2xycos(x2)

    dy/dx = -2xycos(x2) / sin(x2)

    dy/dx=-2xy*Cotx2
     
  7. Oct 15, 2008 #6

    Dick

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    That looks better.
     
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