Derivative of a fraction and power

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SUMMARY

The discussion focuses on finding the derivative of the expression \((\frac{x}{x^2+1})^3\). Participants emphasize the importance of using the chain rule and power rule, followed by the quotient rule for accurate differentiation. Clarification of the expression is crucial, as confusion arises between \((\frac{x}{x^2}+1)^3\) and \((\frac{x}{x^2+1})^3\). Additionally, a suggestion is made to post such questions in the Homework & Coursework section for better guidance.

PREREQUISITES
  • Understanding of the chain rule in calculus
  • Familiarity with the power rule for differentiation
  • Knowledge of the quotient rule for derivatives
  • Ability to clarify mathematical expressions accurately
NEXT STEPS
  • Study the application of the chain rule in complex derivatives
  • Practice problems involving the power rule in calculus
  • Explore the quotient rule through various examples
  • Learn how to properly format and clarify mathematical expressions in forums
USEFUL FOR

Students studying calculus, educators teaching differentiation techniques, and anyone seeking to improve their skills in solving derivative problems.

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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