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Derivative of parametric function

  1. Oct 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the line tangent to the point 2pi/3 when x=cost y=sqrt3 cost.
    Also find the value of d2y/dx2 at the point given.

    2. Relevant equations
    I found dy/dx to be -sqrt3 sint/ -sint. I found that to be just sqrt3. This matched what my calculator told me the slope was. The equation of the tangent is y=sqrt3 x or at least I think.

    I am having trouble with the second derivative. I believe that it is 0. When I applied the quotient rule to dy/dx I got sqrt3 sintcost-sqrt3 sintcost/sin2t. I then multiplied by dt/dx. Either way, the numerator is still 0.

    Am I right, on the right path, or completely wrong.
  2. jcsd
  3. Oct 9, 2008 #2
    I think you're right. d2y/dx2 = 0
  4. Oct 9, 2008 #3


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    Homework Helper

    Yes that is correct. You can get the same answer easily by noting that since dy/dx = constant. Hence d/dx (dy/dx) = 0.
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