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Im confused by this derivative (problem taken from differential equations for dummies

  1. Jul 6, 2009 #1
    1. The problem statement, all variables and given/known data

    The derivative comes from a step in solving a differential equation from the book differential equations for dummies. (if anyone has the book it is in the second chapter page 27).

    d[U(t) y]/dt=U(t) dy/dt+ dU(t) y/dt

    2. Relevant equations

    The original differential that was trying to be solved was dy/dt+2y=4 and he was trying to find the integrating factor, i dont know if that helps at all.

    3. The attempt at a solution

    The reason i dont understand it is because if i were to take the derivative of U(t)*y which im pretty sure is what it is asking i would think that it would simply be the derivative of U(t) times y (dt/dy= U'(t)*y)
     
  2. jcsd
  3. Jul 6, 2009 #2

    Cyosis

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    Homework Helper

    Re: Im confused by this derivative (problem taken from differential equations for dum

    If y would be constant with respect to time your original differential equation would be somewhat trivial wouldn't it be? It would probably not even have a solution. The function you're differentiating is this:

    [tex]
    \frac{d U(t)y(t)}{d t}
    [/tex]

    Use the product rule.
     
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