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Implicit Differentiation

  1. Oct 9, 2005 #1
    Find [tex]\frac{dy}{dx}[/tex] given [tex]cos(y^2) = x^4[/tex]
    Is this correct:

    1. [tex]cos(y^2) = x^4[/tex]

    2. [tex]-sin(y^2) \times 2y \frac{dy}{dx} = 4x^3[/tex]

    3. [tex]\frac{dy}{dx} = \frac{4x^3}{-2sin(y^2)}[/tex]
    Last edited: Oct 9, 2005
  2. jcsd
  3. Oct 9, 2005 #2

    Doc Al

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    Staff: Mentor

    Oops... Looks like you left out a "y" in the last step. Write it like this:
    [tex]\frac{dy}{dx} = -\frac{2x^3}{y \sin(y^2)}[/tex]
    Last edited: Oct 9, 2005
  4. Oct 9, 2005 #3
    Yes, that is what I originally did. The thing is, this is a multiple choice question. Of the choices, the only answers close to this are: (Please don't think I am using this forum for answers. I just believe none of the choices are correct).

    A) [tex]\frac{4x^3}{-sin(y^2)}[/tex]

    B) [tex]\frac{4x^3}{-2ysin(y^2)}[/tex]

    Here are the other choices:

    C) [tex]\frac{\sqrt{xy}-y}{2xy}[/tex]

    D) [tex]\frac{x^4}{-sin(y^2)}[/tex]

    E) [tex]\frac{4x^3}{cos(2y)}[/tex]
  5. Oct 9, 2005 #4


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    Homework Helper

    For the second step, I'd prefer having it written as:

    [tex]-sin(y^2) \times 2y dy = 4x^3dx[/tex]

    This will probably be more consistent once you encounter more complicated problems or do multivariable calculus.

    Answer B is correct. You forgot to move the y over in your last step, step 3.
    Last edited: Oct 9, 2005
  6. Oct 9, 2005 #5

    Doc Al

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    Staff: Mentor

    Right! (I just realized that you left out that y in your last step!)
  7. Oct 9, 2005 #6
    Hehe, how'd that "y" sneak by me? :grumpy:
    Thanks for the help.

    Yeah mezarashi, I am not quite familiar with the notation you used (I just started using the dy/dx notation last week).

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