Product rule. what did I do wrong?

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Homework Help Overview

The discussion revolves around finding the first derivative of the function \( y = (4x - 5)^4 (3x + 1)^5 \) using the product rule. Participants are exploring the expectations of the teacher regarding simplification or factoring of the final answer.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the correctness of the derivative obtained and question whether the teacher expected a specific form of the answer, such as expansion or further factoring.

Discussion Status

Some participants suggest that the original poster's derivative is correct, while others speculate on the teacher's expectations for simplification or factoring. There is no explicit consensus on what the teacher wanted, but various interpretations are being explored.

Contextual Notes

Participants note the difficulty in accessing the teacher for clarification due to scheduling conflicts and the presence of other students seeking help.

tony873004
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It's been too long since I've had an algebra class, so I start getting into trouble as these calculus questions rely more and more on algebra.

[tex] \begin{array}{l}<br /> y = (4x - 5)^4 \,(3x + 1)^5 \\ <br /> {\rm{Find the first derivative}}{\rm{. Simplify if possible (i}}{\rm{.e}}{\rm{. factor)}}{\rm{. Use the product rule}}{\rm{.}} \\ <br /> \left( {(4x - 5)^4 } \right)^\prime \left( {(3x + 1)^5 } \right) + \left( {(4x - 5)^4 } \right)\left( {(3x + 1)^5 } \right)^\prime \\ <br /> \\ <br /> \left( {4(4x - 5)^3 (4x - 5)'} \right)\left( {(3x + 1)^5 } \right) + \left( {(4x - 5)^4 } \right)\left( {5(3x + 1)^4 (3x + 1)'} \right) \\ <br /> \\ <br /> 4(4x - 5)^3 (4)(3x + 1)^5 + (4x - 5)^4 \,\,5(3x + 1)^4 (3) \\ <br /> \\ <br /> 16(4x - 5)^3 (3x + 1)^5 + 15(4x - 5)^4 (3x + 1)^4 \\ <br /> \end{array}[/tex]
I only got 1 point out of 2 on this question. But when I graph it to check the answer, my formula seems to give me the correct slope at all points on the original function. Was the teacher expecting me to simplify this answer?
 
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Yes you have the correct answer. I guess the teacher wanted you to expand, which is silly because it's an 8th degree polynomial with coefficients in the millions.

Maybe he wanted you to factor it even more.

Edit: Well after reading the jibberish you wrote in tex :wink: the problem said to factor the final answer.
 
Last edited:
Perhaps the teacher wanted this:
[tex] \left( {4x - 5} \right)^3 \left( {3x + 1} \right)^4 \left( {16(3x + 1) + 15(4x - 5)} \right)[/tex]
Should I try to factor out the 15 and the 16, which would eliminate one of them, and leave me with a fraction? That would look ugly. Do you suppose the teacher would have wanted this?
 
dav2008 said:
Edit: Well after reading the jibberish you wrote in tex :wink: the problem said to factor the final answer.
Sorry about that. Tex ignored my spaces. From now on, I'll put my text outside the TEX.
 
Well if you just expand that last term you end up with [tex] \left( {4x - 5} \right)^3 \left( {3x + 1} \right)^4 \left( {108x-59} \right)[/tex]

Chances are that's what he was looking for. When in doubt just ask him what he was looking for.
 
Thanks dav2008. His office hours are impossible for me because of work. And there's always a line of students asking q's after class.

Stay tuned for more questions. I'm going over my last 2 tests and trying to figure out all the problems I missed. I might see these on the final!
 

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