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Where did this term go? - Help with Example Problem

  1. Jan 26, 2015 #1
    I'm having trouble figuring out how the term below boxed in red was eliminated on the left side of the equation as shown below. I reviewed properties of exponential functions, and still can't understand how this term was cancelled.

    1. The problem statement, all variables and given/known data

    zwx94z.jpg

    2. Relevant equations
    Exponential laws

    3. The attempt at a solution
    Well e^(a/b) = b root of e^a which is not the case here. I'm not sure how else this term can be written so that it cancels with the tau c below it in the denominator.
     
  2. jcsd
  3. Jan 26, 2015 #2

    kreil

    User Avatar
    Gold Member

    The important equation is 2.12

    The term you're referring to isn't "cancelled", but Eq 2.13 is merely stating that the LHS can be rewritten in terms of the derivative of a product.

    [tex]
    \frac{d}{dt} \left[ f(t)g(t) \right] = \frac{df}{dt}g(t)+\frac{dg}{dt}f(t)
    [/tex]
    If you take the derivative of that product, using the product rule above, then you recover the terms.
    [tex]
    \frac{d}{dt} \left[ h(t) e^{t/{\tau_c}} \right] = \frac{dh}{dt} e^{t/{\tau_c}} + h(t) \frac{d}{dt} \left[ e^{t/{\tau_c}} \right]
    [/tex]
     
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