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Slope of the curve

  1. Oct 16, 2013 #1


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    Gold Member

    1. The problem statement, all variables and given/known data
    Slope of the curve at the point x=0 of the function y=y(x) specified implicitly as [itex]\displaystyle \int_0^y e^{-t^2} dt + \int_0^x \cos t^2 dt = 0[/itex] is

    2. Relevant equations

    3. The attempt at a solution

    Differentiating both sides wrt x
    [itex]e^{-y^2} \frac{dy}{dx} + \cos x^2 = 0[/itex]
    Now If I put x=0 above
    [itex]\dfrac{dy}{dx} = \dfrac{-1}{e^{-y^2}} [/itex]

    But I don't know the value of y when x = 0.
  2. jcsd
  3. Oct 16, 2013 #2


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    Science Advisor
    Homework Helper

    You should be able to figure it out. Put x=0 into your original integral equation.
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