3.2.4 - Quotient Rule
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Practice Questions
Test your understanding with targeted questions
Differentiate \( f(x) = \frac{2x}{x^2 + 3} \) using the Quotient Rule.
💡 Hint: Identify \\( g(x) \\) and \\( h(x) \\) before differentiating.
Find the derivative of \( f(x) = \frac{x^3}{x+1} \).
💡 Hint: Remember the structure of the Quotient Rule: numerator's derivative multiplied by denominator minus the numerator multiplied by the denominator's derivative.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does the Quotient Rule calculate?
💡 Hint: Focus on the nature of the functions involved.
Using the Quotient Rule, how do we represent \( f'(x) \)?
💡 Hint: Keep in mind the structure of the rule you learned.
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Challenge Problems
Push your limits with advanced challenges
Differentiate the function \( f(x) = \frac{x^2 + 1}{sin(x)} \) and simplify your answer.
💡 Hint: Be careful with trig functions as derivatives influence each other.
For the function \( f(x) = \frac{x^3 + cos(x)}{x - 2} \), determine \( f'(x) \).
💡 Hint: Simplifying complex expressions could become tricky; keep your work organized.
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