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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Differentiate \( f(x) = \frac{2x}{x^2 + 3} \) using the Quotient Rule.
💡 Hint: Identify \\( g(x) \\) and \\( h(x) \\) before differentiating.
Question 2
Easy
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.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does the Quotient Rule calculate?
- The derivative of a sum of functions
- The derivative of the product of functions
- The derivative of a quotient of functions
💡 Hint: Focus on the nature of the functions involved.
Question 2
Using the Quotient Rule, how do we represent \( f'(x) \)?
💡 Hint: Keep in mind the structure of the rule you learned.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation