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Find equation of tangent line of tan(xy^2)=(2xy)/pi (implicit diff.)

  1. Oct 28, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the equation of the tangent line of tan(xy2)=(2xy)/[itex]\pi[/itex] at (-[itex]\pi[/itex],1/2)

    2. Relevant equations



    3. The attempt at a solution

    I managed to get the equation into its dy/dx form and for the slope to be (1-.5pi)/(2pi-2pi2)
    This seems far to complicated to be correct though.. can someone confirm this?
     
    Last edited: Oct 28, 2012
  2. jcsd
  3. Oct 28, 2012 #2

    SammyS

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    Please show your result for implicit differentiation prior to substituting for the given point. I get something different for y' at that point, but it's similarly complicated.
     
  4. Oct 28, 2012 #3
    Here's what I got, dy/dx = [y2(pi)sec2(xy2)-2y]/[(2x)(1-y(pi)sec2(xy2)]
     
  5. Oct 28, 2012 #4

    SammyS

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    I checked your (implicit) differentiation and the value of the derivative at (-π, 1/2) with WolframAlpha, and it agrees with your results totally.
     
  6. Oct 28, 2012 #5
    That's always good to hear :p So my slope I found is most likely right? Even tho its a mess to look at?
     
  7. Oct 28, 2012 #6

    SammyS

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    Yes, I'm quite sure that it's correct.
     
    Last edited: Oct 28, 2012
  8. Oct 28, 2012 #7
    Ok, thank you !
     
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