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Quick question about the derivative of a complex-valued function

  1. Feb 20, 2010 #1
    This is something that has been bothering me for awhile. Suppose we have some function f(x) = u(x) + iv(x), where u,v are real-valued functions. Obviously Re(f) = u(x) and Im(f) = v(x), both of which are real. My question is: in general, is it safe to say that

    [tex]\frac{d}{dx} Re(f) = Re\left(\frac{df}{dx}\right)[/tex]

    ? If so, that makes life a lot easier with trig identities dealing with derivatives. This seems really trivial, and I feel like it's correct, but I can't figure out how one would prove it, and I don't want to use it just assuming that it is true...

    Thanks!
     
  2. jcsd
  3. Feb 20, 2010 #2

    tiny-tim

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    Hi tjackson3! :smile:

    no problem … df(x)/dx = du(x)/dx + idv(x)/dx,

    and if u,v (and x) are real-valued functions, then so are du(x)/dx, dv(x)/dx. :wink:
     
  4. Feb 21, 2010 #3
    tjackson3, is x a real variable?
     
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