Optimizing the Product Rule: Common Error Help for (5x-2)^3 / (2x+5)^4

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Homework Help Overview

The discussion revolves around differentiating the function y = (5x-2)^3 / (2x+5)^4 using the product rule. Participants are examining the differentiation process and identifying potential errors in the original poster's approach.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants are analyzing the differentiation steps provided by the original poster, questioning the correctness of the derivatives calculated for both f(x) and g(x). There is a focus on the application of the product rule and the derivatives of the individual functions.

Discussion Status

Some participants have pointed out possible errors in the differentiation process, leading to a correction in the derivative calculations. There is acknowledgment of these errors, but no consensus on the final correct approach has been reached yet.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the extent of guidance provided. The original poster's differentiation steps are under scrutiny, and assumptions about the application of the product rule are being questioned.

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y = ( 5 x-2 ) 3 / ( 2 x+5 ) 4

I do it this way:

f(x) = (5x-2)3
g(x) = (2x+5)-4
f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5

By using the product rule:

[3(5x-2)2](2x+5)-4 + (5x-2)3[-4(2x+5)-5]
3(5x-2)2(2x+5)-4 -4(2x+5)-5(5x-2)3

What's wrong with this answer?
 
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Thread moved to Homework Help

f'(x) = 3(5x-2)2
g'(x) = -4(2x+5)-5

I do not believe you have differentiated correctly in these steps.
 


Is it this way??

f'(x) = 15(5x-2)2
g'(x) = -8(2x+5)-5
 
Last edited:


Yes, got it. Thanks for pointing out the error.
 

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