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Differentiate e^x and Trig Functions

  1. May 3, 2010 #1
    1. The problem statement, all variables and given/known data
    e^x * cotx / 5sqrtx^2
    [Sorry for not using the formatting things. They didn't seem to be working for me, and this is urgent!]

    2. Relevant equations
    The quotient rule seems like that's the way to go...

    3. The attempt at a solution
    At first I tried using the product rule on the numerator, then plugging that into the quotient rule formula, but that was needlessly complicated. So, I went straight into using the quotient rule, but I got a huge messy equation. Could anyone clarify what I SHOULD be getting?

    All help is greatly appreciated!
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. May 3, 2010 #2
    Both ways are correct. Either do product rule inside of Quotient or do Product then do Quotient. Both will be potentially messy.
  4. May 3, 2010 #3
    also is that 5sqrt(x^2) or (5sqrt(x))^2 or what?
    because that should simple things out for you.
  5. May 3, 2010 #4
    It's 5sqrt(x^2).
    Sorry about that.
  6. May 3, 2010 #5
    The quotient rule is never worth remembering IMO. Just use the product rule and think of the derivative of a quotient as

    \frac{d}{dx}\left( \frac{f(x)}{g(x)} \right) = \frac{d}{dx}\left(f(x) \ g(x)^{-1}\right)

    and dont forget to apply the chain rule when differentiating [tex]g(x)^{-1}[/tex].

    It's too easy to forget the quotient rule on an exam, and also too easy to screw it up when you're in a rush to get everything done in 50 minutes on a midterm. The product rule and chain rule are easy though, and critical to know anyways.
  7. May 3, 2010 #6
    What's the square root of x^2?

    that will make it a little simpler.
    Last edited: May 3, 2010
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