How to Use Quotient and Product Rule to Find Derivatives | First Derivative Help

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SUMMARY

The discussion focuses on differentiating the function AC = (Q + 1)^(0.5) / Q using both the quotient rule and product rule. The correct application of the product rule yields the derivative dac/dQ = Q^(-1.5) + 1 + 0.5(Q + 1)^(1/2). Participants emphasize that both differentiation methods should yield equivalent results, demonstrating the relationship between the two approaches. Clarification is sought on the expressions derived from each rule to ensure understanding of their equivalence.

PREREQUISITES
  • Understanding of calculus concepts, specifically differentiation.
  • Familiarity with the quotient rule and product rule for derivatives.
  • Knowledge of algebraic manipulation and simplification techniques.
  • Ability to work with fractional exponents and their derivatives.
NEXT STEPS
  • Study the application of the quotient rule in detail with examples.
  • Explore the product rule and practice differentiating various functions.
  • Learn about simplifying derivatives involving fractional exponents.
  • Review calculus textbooks or online resources for additional practice problems on derivatives.
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Students studying calculus, particularly those learning about differentiation techniques, as well as educators looking for clear explanations of the quotient and product rules.

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Homework Statement


differentiate the following function using both the quotient and product rule with respect to their independent variable(s) and simplify your answer


Homework Equations


AC= (Q+1)^(0.5) / Q


The Attempt at a Solution


product rule:
dac/dQ = [(Q+1)^(0.5) x (-q^-2) ] + [ 0.5(Q+1)^(1/2) ]
dac/dQ = Q^(-1.5) + 1 + 0.5(Q+1)^(1/2)
 
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I think you are just supposed to show that d/dQ of (Q+1)^(1/2)/Q taken with the quotient rule, and d/dQ of (Q+1)^(1/2)*Q^(-1) taken with the product rule are equal. But I'm really not sure how you are getting those expressions you show. Can you show us?
 

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