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Re: Derivative of a Conjugate

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  • Subject: [mg87244] Re: Derivative of a Conjugate
  • From: dh <dh at>
  • Date: Sat, 5 Apr 2008 04:23:25 -0500 (EST)
  • References: <ft4n6o$3vk$>

Hi David,

Conjugate is not an analytic function. Consider:

r=x+I y; z[r]= x+I y; Conjugate[z[r]]= x-I y;

dz= dx + I dy; dConjugate[z]= dx -I dy

now take the differential quotient and you see that the derivative 

depends on the direction. That is why Mathematica does not evaluate 


If dr is real you may e.g. use a rule to get what you want:

expression /. Conjugate'[y_[x_]]:= Conjugate[y'[x]]

hope this helps, Daniel

David Forehand wrote:

> Hi All,


> My first posting here, so please forgive me if I am being a bit stupid.


> I'm entering the following input:


> D[f[t0, t1], t0, t1] /. {f -> ((#1^2)*Conjugate[a[#2]] &)}


> and Mathematica gives the following output:


> 2 t0 a'[t1] Conjugate'[a[t1]]


> I would have expected:


> 2 t0 Conjugate[a'[t1]]


> i.e. the derivative of a conjugate is the conjugate of the derivative.


> Any idea how a force Mathematica to give the result I am expecting?  In the above, I am assuming the variables "t0" and "t1" are real and the variable "a" is complex, although I have not explicitly told Mathematica this.


> Thanks Very Much in advance,


> David


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