Understanding the Role of n in the Denominator of Fourier Series

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SUMMARY

The discussion centers on the role of 'n' in the denominator of the Fourier series, specifically in the context of differentiating the function \(\frac{\sin(nx)}{n}\). Participants highlight the importance of understanding the reverse chain rule and suggest using u-substitution as a method to simplify the differentiation process. The conversation emphasizes that grasping u-substitution is crucial for effectively handling such problems in calculus.

PREREQUISITES
  • Understanding of Fourier series concepts
  • Knowledge of differentiation techniques, including the reverse chain rule
  • Familiarity with u-substitution in calculus
  • Basic trigonometric functions and their derivatives
NEXT STEPS
  • Study the application of the reverse chain rule in calculus
  • Learn about u-substitution techniques for integration and differentiation
  • Explore the properties of Fourier series and their applications
  • Review trigonometric derivatives and their implications in calculus
USEFUL FOR

Students studying calculus, particularly those focusing on Fourier series, as well as educators looking to clarify concepts related to differentiation and substitution methods.

robertjford80
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Homework Statement



Screenshot2012-06-15at30300AM.png





The Attempt at a Solution



I don't see why the n is in the denominator
 
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reverse chain rule. What's the derivative of [itex]\frac{\sin(nx)}{n}?[/itex]

If that doesn't make sense, then...

you could use u-substitution to avoid going backwards.

If you don't know u-substitution, that can be part of the problem.
 
thanks, got it
 

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