Find and simplify the derivative (quotient rule)

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SUMMARY

The discussion focuses on finding and simplifying the derivative of the function (x² - 3)⁴/(2x³ + 1)³ using the quotient rule. The initial derivative calculation yields 8x(x² - 3)³ - 18x²(2x³ + 1)²/(2x³ + 1)⁶, which is not in simplified form. Participants emphasize the importance of systematic approaches to tackle complex derivatives, suggesting the use of u and v substitutions for clarity in differentiation.

PREREQUISITES
  • Understanding of calculus, specifically differentiation techniques.
  • Familiarity with the quotient rule for derivatives.
  • Knowledge of algebraic manipulation for simplification.
  • Experience with function notation and substitution methods.
NEXT STEPS
  • Study the application of the quotient rule in calculus.
  • Learn about algebraic simplification techniques for derivatives.
  • Explore the use of u-substitution in differentiation.
  • Practice with complex derivative problems to enhance problem-solving skills.
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Students studying calculus, particularly those learning about derivatives and simplification techniques, as well as educators looking for effective methods to teach these concepts.

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Homework Statement



find the derivative of (x2 - 3)4/(2x3+1)3

and simplify

Homework Equations





The Attempt at a Solution



as far as i could get was 8x(x2-3)3-18x2(2x3+1)2/(2x3+1)6

which is not simplified.

How can you simplify something like this? Is there a systematic way to approach it?

In general, what is the best method to approach really messy derivatives (such as this one, or any other that can be manipulated by algebra)?
 
Last edited:
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Check your calculation: [tex]u=(x^{2}-3)^{4}[/tex] and [tex]v=(2x^{3}+1)^{3}[/tex], then:
[tex] \frac{du}{dx}=8x(x^{2}-3)^{3}\quad\frac{dv}{dx}=18x^{2}(2x^{3}+1)^{2}[/tex]
From here the algebra is doable.
 
Doh. Thanks lol
 

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