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Calculate the derivative

  1. Jun 17, 2004 #1
    I have to calculate the derivative of this function:

    [tex] f(t)=\vert\hspace{0.07cm}u(t)+i\cdot{}v(t)\vert [/tex]

    The derivative should be expressed with u, u', v and v'.
    How do you calculate this derivative?
     
  2. jcsd
  3. Jun 17, 2004 #2
    Okay, this is a combination of the chain rule and implicit differentiation.

    The first thing to do is let [tex]a=u(t)+iv(t) [/tex]

    Now let [tex]f(x)=\sqrt{a^2}[/tex] and the derivative becomes

    [tex]\frac{df}{dt}=\frac{df}{da}\frac{da}{dt}[/tex]

    You should be able to proceed from there. If not, yell out.
     
  4. Jun 17, 2004 #3

    Gokul43201

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    But [tex] \vert\hspace{0.07cm}u(t)+i\cdot{}v(t)\vert = u^2(t) + v^2(t)[/tex]

    So, [tex] f'(t) = 2(uu' +vv') [/tex]


    EDIT : forgot SQRT, but Hurkyl got it !
     
  5. Jun 17, 2004 #4

    Hurkyl

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    That won't work at all. In particular, [itex]f = \sqrt{a^2}[/itex] is incorrect and [itex]df/da[/itex] does not exist.


    The most straightforward way to compute this derivative is to simply write out the function f. You recall that [itex]|x + iy| = \sqrt{x^2 + y^2}[/itex], right? Apply the definition of modulus, and you should get something you could do back in calc I.
     
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