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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Differentiate \( f(x) = x^2 ext{sin}(x) \).
💡 Hint: Identify the two functions to differentiate.
Question 2
Easy
Differentiate \( f(x) = 3x^3 ext{cos}(x) \).
💡 Hint: Remember to differentiate both parts of the product.
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 is the Product Rule used for?
- Finding square roots
- Finding derivatives of products of functions
- Adding functions
💡 Hint: Think about its application in calculus.
Question 2
True or False: The Product Rule states that differentiation of a product is the sum of the derivatives.
- True
- False
💡 Hint: Recall the formula.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
If \( f(x) = (x^2 + 1)( ext{sin}(x) + x) \), find \( f'(x) \).
💡 Hint: Remember to apply Product Rule carefully and simplify your answer.
Question 2
Differentiate \( f(x) = e^x ext{cos}(2x) \).
💡 Hint: Don't forget the chain rule when dealing with \\( ext{cos}(2x) \\).
Challenge and get performance evaluation