Mastering Partial Differentiation: A Comprehensive Guide

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Discussion Overview

The discussion revolves around the topic of partial differentiation, with participants seeking assistance on a specific problem related to differentiation and integration. The scope includes mathematical reasoning and clarification of concepts related to these operations.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty in solving a problem related to partial differentiation and requests help.
  • Another participant claims to have found the answer to the question, though the details of this answer are not fully elaborated.
  • A mathematical expression involving differentiation and integration is presented, suggesting a relationship between the functions involved.
  • One participant argues that the problem pertains to "integration by parts" rather than "partial differentiation," indicating a potential misunderstanding or misclassification of the problem.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there is disagreement regarding whether the problem is about partial differentiation or integration by parts.

Contextual Notes

The discussion lacks clarity on the specific problem being addressed, and there may be missing assumptions regarding the definitions of the functions involved. The mathematical steps presented are not fully resolved.

jaychay
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Untitled 4.png


Can you please help me ?
I have tried to do it many times but I end up getting the wrong answer.
Thank you in advance.
 
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I finally got the answer to the question.
Untitled 5.png
 
$\dfrac{d}{dx}[f(x)h(x)] = f’(x)h(x) + f(x)h’(x)$

$\displaystyle f(x)h(x) = \int f’(x)h(x) \, dx + \int f(x)h’(x) \, dx$

$\displaystyle (x+1)^5 = \sin{x} + \int f(x)h’(x) \, dx$

finish it ...
 
I think this is a problem on "integration by parts", NOT "partial differentiation".
 

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