1) Which rule is used to differentiate the function f(x) = x⁵ + 3x²? a) Product Rule b) Quotient Rule c) Power Rule d) Chain Rule 2) What is the derivative of f(x) = (2x + 1)(x - 3)? a) Use the sum rule b) Use the product rule c) Use the chain rule d) Use the constant rule 3) If f(x) = √5x + 1, which rule is needed to find f'(x)? a) Chain Rule b) Power Rule c) Product Rule d) Quotient Rule 4) What rule is applied when finding the derivative of f(x) = x²+1/x+3? a) Sum Rule b) Chain Rule c) Quotient Rule d) Constant Rule 5) What is the derivative of a constant multiplied by a function, such as f(x) = 7x²? a) Add 7 to the derivative of x² b) Multiply 7 by the derivative of x² c) Subtract 7 from the derivative of x² d) Ignore the constant 6) What rule is used to integrate ∫ (x³ + 2x) dx? a) Product Rule b) Chain Rule c) Sum Rule d) Quotient Rule 7) When integrating a constant like ∫ 5 dx, which rule do you use? a) Power Rule b) Chain Rule c) Constant Rule d) Product Rule 8) What is the integral of 3x², and what rule is used? a) x³ + C; Power Rule b) 3x³ + C; Product Rule c) x² + C; Constant Rule d) 3/2x + C; Sum Rule 9) To evaluate the ∫ x(x² + 1) dx, which method is best? a) Use substitution b) Use the chain rule c) Use partial fractions d) Use the quotient rule 10) Which rule explains why ∫ (2x² + 4x + 6) dx = ⅔x³ + 2x² + 6x + C? a) Chain Rule b) Power Rule And Sum Rule c) Product Rule d) Constant Rule Only

Calculus

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