Derivative of a fraction and power

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Discussion Overview

The discussion revolves around taking the derivative of the expression \((\frac{x}{x^2+1})^3\). Participants explore different approaches to differentiate this expression, including the use of the chain rule, power rule, and quotient rule.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant suggests starting with the difference quotient as a general approach to derivatives.
  • Another participant interprets the expression as \((\frac{x}{x^2}+1)^3\) and recommends using the chain rule along with the power and quotient rules.
  • A clarification is requested regarding the expression, asking whether it is \((\frac{x}{x^2+1})^3\) or \((\frac{1}{x}+1)^3\).
  • A participant notes the importance of posting such questions in the Homework & Coursework section for better guidance.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct interpretation of the expression, and there is no agreement on a single method to approach the derivative. The discussion remains unresolved regarding the best starting point for differentiation.

Contextual Notes

There are ambiguities in the expression being differentiated, which affect the approach to finding the derivative. The discussion does not resolve these ambiguities.

Latte'
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I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
 
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Start as how you start to any derivative, difference quotient.
 
as I interpret
$$(\frac{x}{x^2}+1)^3$$

start with the chain rule with power rule , then quotient and difference rule .
 
Latte' said:
I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
Start by clarifying your expression.
(\frac{x}{x^2+1})^3 or (\frac{1}{x}+1)^3?
 
Thanks! That really helped.
 
Latte' said:
I'm trying to take the derivative of [x/x^2+1]^3. Where do I start?
In the future, post questions like this in the Homework & Coursework section (under Calculus), not here in the technical sections. When you post a question in the Homework section, a template appears into which you enter the problem description, any formulas or equations, and what you have tried.
 

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