1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    gb7nash

    User Avatar
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

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

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

    [tex]y'+2xy=1[/tex]

    I was concerned that the integral still containing the "t" variable wouldn't cancel, however upon re-inspection I think it should.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivative Problem
  1. Derivation Problem (Replies: 3)

  2. Derivative problem (Replies: 4)

  3. Derivative problem (Replies: 3)

  4. Derivative problem (Replies: 10)

  5. Derivative problem (Replies: 9)

Loading...