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Homework Help: Derivative Problem

  1. Sep 18, 2011 #1
    I'm unsure of my work when completing this problem:

    [tex]y=e^{-x^{2}} \int^{x}_{0} e^{t^{2}} dt + c_{1}e^{-x^{2}}[/tex]

    I applied the product rule to the left bit.

    [tex]\frac{dy}{dx}=e^{-x^{2}} e^{x^{2}} + e^{-x^{2}}(-2x)\int^{x}_{0} e^{t^{2}} dt + (-2x)c_{1}e^{-x^{2}}[/tex]

    I'm fairly certain I did this wrong.
  2. jcsd
  3. Sep 18, 2011 #2
    I believe that:
    [tex] \int^{x}_{0} e^{t^{2}} dt [/tex]
    Is a constant with respect to x, so you don't need to use the product rule, just treat it like any other constant
  4. Sep 18, 2011 #3


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    No, this is a function with respect to x, so the product rule is valid here.
  5. Sep 18, 2011 #4
    So I derived it correctly?
  6. Sep 18, 2011 #5

    Ray Vickson

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    I'm certain you did it right. Why do you think otherwise?

  7. Sep 18, 2011 #6
    It's from a problem where I need to verify that it is a solution to:


    I was concerned that the integral still containing the "t" variable wouldn't cancel, however upon re-inspection I think it should.
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