Derivative using complex exponential

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Homework Help Overview

The discussion revolves around finding the 15th derivative of the function exp[(1 + i(3^.5))theta] with respect to theta, which involves complex exponentials and their derivatives.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to determine if splitting the exponential into two parts is necessary. Other participants raise questions about the general properties of derivatives of exponential functions and suggest applying standard rules for derivatives.

Discussion Status

Participants are exploring different approaches to the problem, including the application of De Moivre's formula and the properties of derivatives of exponential functions. There is no explicit consensus, but guidance on using known mathematical principles has been provided.

Contextual Notes

Some participants question the need for splitting the exponential and discuss the implications of treating complex numbers as constants in differentiation.

forty
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I'm trying find the 15th derivative of exp[(1 + i(3^.5))theta] with respect to theta

To do this do i need to split it into two exponentials, (e^theta).(e^i(3^.5)theta) ??
 
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What is the derivative of eax with respect to x? What is its second derivative? What is its 15th derivative? Do you see my point?
 
[(1+i(3^.5))^15].e^[(1+i(3^.5))theta]

So i can just apply the normal rules for exponentials ??
 
Yes, 1+i(3^.5) is "just a number". You might want to use De Moivre's formula to caculate [itex](1+ i\sqrt{3})^{15}[/itex] itself.
 

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