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Implicit Differentiation

  1. Oct 17, 2008 #1
    1. The problem statement, all variables and given/known data
    Use implicit differentiation to find the slope of the tangent line to the curve

    4x^2-3xy+1y^3=26

    at the point (3,2)

    3. The attempt at a solution
    I attempted the problem and i came up with dy/dx= (-8x+4)/(3y^2) which is wrong.

    Need some help with this.
     
  2. jcsd
  3. Oct 17, 2008 #2

    Dick

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    How did you get that?
     
  4. Oct 17, 2008 #3

    HallsofIvy

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    Then show us HOW you got that answer!

    I suspect you may have messed up a "product rule" but I can't be sure unless you show exactly what you did.
     
  5. Oct 17, 2008 #4
    This is what i did:

    It sounds totally wrong and it looks wrong but i didn't know what to do



    (d/dx)(4x^2-3xy+1y^3)=26
    (dy/dx)(3y^2)=-8x+4
    dy/dx=(-8x+4)/(3y^2)
     
  6. Oct 17, 2008 #5

    djeitnstine

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    For your 3xy term you have to use the product rule.... you will find that it will turn out to be -[ (3 dx/dx y') + (3x y') ] product rule being f'g + fg' y' being dy/dx of course
     
  7. Oct 17, 2008 #6
    I still don't get what you mean. When i differentiate 3xy using the product rule, what should i get? Am i supposed to get (3*(xy)) - (3x*1)? I don't completely get the concept
     
  8. Oct 17, 2008 #7

    djeitnstine

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    differentiating 3xy using the product rule (f'g + fg' - in words this is the derivative of f times g plus f times the derivative of g) looks like this [tex]3y\frac{dx}{dx}[/tex] + [tex]3x\frac{dy}{dx}[/tex] Which leaves you with [tex]3y + 3x\frac{dy}{dx}[/tex]
     
  9. Oct 17, 2008 #8
    Ahhh, I see what you mean now. I did everything, but for the final slope i get -30/21. I have no idea how it's wrong when I did exactly what you told me.
     
  10. Oct 17, 2008 #9

    djeitnstine

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    also don't forget that the y^3 differentiates to (3y^2) * (y')
     
  11. Oct 17, 2008 #10
    I was finally able to get the answer which was -6. Thank you very much for the help.
     
  12. Oct 17, 2008 #11

    djeitnstine

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    No problem
     
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