How to Correctly Apply the Power Rule in Calculus?

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SUMMARY

The discussion focuses on the correct application of the Power Rule in calculus, specifically for the function y = (x^5/6) + (1/10x^3). The initial derivative attempt of 5X^4 - 30X^2 is confirmed to be incorrect. The correct application of the Power Rule results in the derivatives of each term being 5/6 * x^(5/6 - 1) and -3/10 * x^(-4), respectively. Participants emphasize the importance of accurately interpreting the original equation for proper differentiation.

PREREQUISITES
  • Understanding of basic calculus concepts, specifically differentiation.
  • Familiarity with the Power Rule for derivatives.
  • Knowledge of algebraic manipulation of polynomial expressions.
  • Ability to interpret mathematical notation accurately.
NEXT STEPS
  • Review the Power Rule in calculus for various polynomial functions.
  • Practice differentiating complex functions involving multiple terms.
  • Explore common mistakes in applying the Power Rule and how to avoid them.
  • Learn about higher-order derivatives and their applications in calculus.
USEFUL FOR

Students studying calculus, mathematics educators, and anyone looking to improve their skills in differentiation and understanding of the Power Rule.

FARADAY JR
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Homework Statement


y=(X^5/6) + (1/10X^3)


Homework Equations





The Attempt at a Solution


5X^4 - 30X^2
 
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can anyone please confirm it so I can proceed with the problem. thank you
 
Without tex it is hard to see what the original equation is. Either way, both terms look incorrect. Was this your original equation?

[tex]y = \frac{x^5}{6} + \frac{1}{10 x^3}[/tex]

What does the power rule say for derivatives?
 

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