Need help with using Leibniz's Rule

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Discussion Overview

The discussion revolves around the application of Leibniz's Rule in calculating the derivative of an integral function. Participants are attempting to solve a specific mathematical problem involving the function g(x) defined by an integral and are comparing their results.

Discussion Character

  • Mathematical reasoning, Homework-related, Debate/contested

Main Points Raised

  • One participant expresses confusion over their solution to the problem, stating they obtained 7e4/2 instead of the expected e4.
  • Another participant agrees with the first, suggesting they may have made a similar mistake or that the problem might have been misinterpreted as asking for g(2) instead of g'(2).
  • A third participant reiterates the same concern about possibly misinterpreting the question, emphasizing that the question explicitly asks for g'(2).
  • A later reply suggests that if g(x) is considered only as the integral, then the derivative at x=2 is e^4, hinting at a possible transcription error in the original calculations.

Areas of Agreement / Disagreement

Participants generally agree that there may be a misunderstanding regarding the question or a mistake in their calculations, but no consensus is reached on the correct answer or the source of the error.

Contextual Notes

There is uncertainty regarding the interpretation of the problem and the calculations involved, with participants acknowledging the possibility of errors in their approaches or in the question itself.

Astro
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I tried solving this question but I'm not getting the correct answer and I don't know what I'm doing wrong. Can anyone tell me what I did wrong? Thank you.

The math question is:
Let g(x) = d/dx (∫x21 et/t dt), then g'(2) is ____?

The correct answer is e4 but I'm getting 7e4/2. (See my solution attempt in the attached PDF file.)
 

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I get the same result as you. Maybe we made the same mistake, or maybe the question was to find ##g(2)##.
 
Samy_A said:
I get the same result as you. Maybe we made the same mistake, or maybe the question was to find ##g(2)##.
Thank you for your reply.
The sample question specifically asks for g'(2) but what you say seems to make sense.
(Although, that would be a he** of a mistake on the part of the school since it's the one of last year's exam questions. :/ )
 
Astro said:
Thank you for your reply.
The sample question specifically asks for g'(2) but what you say seems to make sense.
(Although, that would be a he** of a mistake on the part of the school since it's the one of last year's exam questions. :/ )
Well, everybody can make mistakes. Maybe we did, maybe the school did. Let's wait for others to check the computation.
 
If you let g(x) be the integral only. Then the derivative of g(x) at x=2 is e^4. Probably transcription error somewhere.
 

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