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F(x)=2xe^(-x) what is derivative?

  1. Dec 15, 2004 #1
    f(x)=2xe^(-x)

    what is derivative?

    [tex]f(x)=(2x)/(e^x)[/tex]
    [tex]f'(x)={{2e^x}-{2x^2e^{x-1}}}/(e^x)^2[/tex]

    can I simplify this?
     
  2. jcsd
  3. Dec 15, 2004 #2

    Integral

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    Recall that:
    [tex] \frac {d e^x} {dx} = e^x [/tex]
    then apply the chain rule.
     
    Last edited: Dec 15, 2004
  4. Dec 15, 2004 #3

    FZ+

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    Surely easier to do by product rule!

    [tex]f'(x)=2e^-^x - 2xe^-^x[/tex]

    or even:

    [tex]f'(x)=(2 - 2x)e^-^x[/tex]
     
    Last edited: Dec 15, 2004
  5. Dec 15, 2004 #4
    gee thanks!
    The questions acually asks to find each critical point of f and whether f(x) is a relative maximum, relative minimum, or neither. I set f'(x) to zero and solved. I got x=1.

    I found it to be a maximum value. Is this correct?
     
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