Derivative of the Real Part of a Complex Function (Mathematica)

In summary, the derivative of the real part of a complex function is the real part of the derivative of the complex function. It can be calculated in Mathematica using the Re[D[f[z],z]] command and can be represented graphically by plotting the real part of the derivative function. The derivative of the real part is important in understanding the behavior of the complex function and can help identify critical points such as maxima, minima, and inflection points. There are special cases when calculating the derivative, such as when the complex function is purely real or imaginary.
  • #1
Swamp Thing
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Why doesn't this work:
D [ Re[ Exp[u + 10*I] ], u ] /. u->0.5
When I type in this:
Code: 
D [
      Re[
           Exp[u + 10*I]
        ],
           u
   ]    /.  u->0.5
I get this output:
1584851721030.png


Of course, I could just put the Re outside and the D inside, but it would be nice to know what is wrong with the above. What's with the Re' in the output?
 
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  • #3
Mathematica.
 
  • #4
Mathematica doesn’t know that you intend u to be real.
 
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1. What is the derivative of the real part of a complex function?

The derivative of the real part of a complex function is essentially the same as the derivative of a regular real-valued function. It is a measure of how the real part of the function changes with respect to its input, which can be a complex number.

2. How do I calculate the derivative of the real part of a complex function in Mathematica?

In Mathematica, the derivative of the real part of a complex function can be calculated using the function Re'[z], where z is the complex function. This will return the derivative of the real part of the function with respect to its input.

3. Can the derivative of the real part of a complex function be complex?

Yes, the derivative of the real part of a complex function can be complex. This is because the derivative is a measure of how the real part of the function changes with respect to its input, which can be a complex number. So, the derivative can also be a complex number.

4. What does the derivative of the real part of a complex function tell us?

The derivative of the real part of a complex function tells us how the real part of the function changes with respect to its input. It can be used to find the rate of change of the real part of the function at a specific point, as well as the slope of the tangent line at that point.

5. Can I use the derivative of the real part of a complex function to find critical points?

Yes, the derivative of the real part of a complex function can be used to find critical points, which are points where the derivative is equal to zero. These points can be important in determining the behavior of the function, such as local maxima or minima.

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