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1st derivative

  1. May 27, 2006 #1
    Differentiate the function: f(u) = e1/u
    So, I used the chain rule and figured out that
    f '(u) = (-u-2) e1/u

    My question is, why do you have to use the chain rule?
    I know that if f(x) = ex
    then f '(x) = ex

    Why can't I pretend that 1/u is x and then say that
    f '(x) = ex = e1/u

    In other words, does the exponent always have to be "x" only, for f '(x) = ex to work?
  2. jcsd
  3. May 27, 2006 #2
    The derivative e^u with respect to u is e^u and the derivative e^x with respect to x is e^x, and it does not matter what alpahbet you choose to denote the variable with. It's a dummy.

    But in the problem you have posted, if you assume that x = 1/u, then the function is f(x(u)) [since x is now a function of u], and that is why you use the chain rule. You assume it to be a fucntion of a fucntion. Therefore [tex]\frac{df}{du} = \frac{df}{dx}\frac{dx}{du}[/tex]
  4. May 27, 2006 #3
    Oooh, ok, thanks
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