Wierd Q to take a derivative of

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    Derivative
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Discussion Overview

The discussion revolves around the process of taking the derivative of the function y=(x)/((x+2)(x+3)(x+4)). Participants seek guidance on the appropriate methods and rules to apply for differentiation, including the quotient rule and product rule.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant asks for help in taking the derivative of the function, expressing confusion about the process.
  • Another participant suggests using the quotient rule and Leibniz product rule for differentiation.
  • A different participant emphasizes the importance of avoiding multiple posts in the thread.
  • One suggestion is to rewrite the function to facilitate differentiation using the product of inverse functions.
  • Another participant proposes multiplying out the denominator to simplify the function before applying the product rule and provides a derivative formula for the reciprocal function.
  • Some participants engage in light-hearted banter regarding the posting etiquette and learning from mistakes.

Areas of Agreement / Disagreement

There is no clear consensus on the best method for taking the derivative, as participants suggest different approaches and rules without resolving which is superior.

Contextual Notes

Participants express varying levels of familiarity with differentiation techniques, and there may be assumptions about prior knowledge of calculus concepts that are not explicitly stated.

the4thcafeavenue
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weird Q to take a derivative of...

y=(x)/((x+2)(x+3)(x+4)).
how to do u take the derivative? HELP! :confused:
 
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So is it

y(x)=\frac{x}{(x+2)(x+3)(x+4)}

Do u know to apply the

1.Quotient's derivative rule.
2.Leibniz product rule...?

Daniel.
 
AARGH!

DO NOT DOUBLE, TRIPLE, OR QUADRUPLE POST IN THE FUTURE!
 
The easiest way would be to rewrite it like this first:

y=(x) * (x+2)(^-1) * (x+3)(^-1) * (x+4)(^-1)
 
haha, i guess i'd get mroe help dat way, but, oops hehe
 
the easiest way is actually probably to just multiply out the denominator:

\frac{x}{(x+2)(x+3)(x+4)} = \frac{x}{x^3 + 9x^2 + 26x + 24}

and then just use the product rule and the fact that

\frac{d}{dx}\frac{1}{f(x)} = -\frac{f^\prime (x)}{\left[f(x)\right]^2}
 
the4thcafeavenue said:
haha, i guess i'd get mroe help dat way, but, oops hehe
At least, now you've learned your lesson, right? :wink:
 

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