Need help with using Leibniz's Rule

  • Thread starter Astro
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In summary, the conversation revolved around a math question asking for g'(2), which was supposed to be e^4 but the participants were getting 7e^4/2. They discussed the possibility of making a mistake or the question being written incorrectly. Eventually, it was determined that the correct answer should be e^4, indicating a possible transcription error.
  • #1
Astro
48
1
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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  • #2
I get the same result as you. Maybe we made the same mistake, or maybe the question was to find ##g(2)##.
 
  • #3
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. :/ )
 
  • #4
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.
 
  • #5
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.
 

1. What is Leibniz's Rule?

Leibniz's Rule, also known as the product rule, is a mathematical formula used to find the derivative of a product of two functions. It is named after the German mathematician and philosopher Gottfried Wilhelm Leibniz.

2. When should Leibniz's Rule be used?

Leibniz's Rule is used when we want to find the derivative of a product of two functions, where both functions are dependent on the same variable. It is especially useful when finding the derivatives of complicated functions.

3. How do you use Leibniz's Rule?

To use Leibniz's Rule, we first write out the two functions that we want to find the derivative of. Then, we use the formula: d/dx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x), where f'(x) represents the derivative of the first function and g'(x) represents the derivative of the second function. We then plug in the values for each function and simplify the equation to find the final derivative.

4. What are the common mistakes when using Leibniz's Rule?

One common mistake when using Leibniz's Rule is forgetting to apply the chain rule when finding the derivatives of the individual functions. It is also important to pay attention to the order of the terms in the formula, as switching the order can result in an incorrect answer.

5. Can Leibniz's Rule be used for more than two functions?

Yes, Leibniz's Rule can be extended to find the derivative of a product of three or more functions. However, it can become more complicated and time-consuming, so it is often more efficient to use other methods such as the chain rule or product rule for these cases.

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