Basic Calculus, Derivative Rules

MULTIPLE CHOICE: Write the capital letter of the best answer in the space provided before the number. 1. Suppose f (x) = x2 (x2 + 1), determine f'(2) ? A. 48 B. 36 C. 24 D. 12 2. Choose the best solution for the derivative of f (x) = *+2 (x-3)-(x+2) B. (x+2)-(x-3) C. (x-3) -(x+2) D. (x+2) -(x-3) (x-3)2 (x-3)2 (x+ 2)2 (x+2)2 3. Find the derivative of f (x) = (x6 + 4)5 A. f' (x) = 5x5 (x4+ 4)4 C. f' (x) = 6x5 (x6 + 4)4 B. f' (x) = 30x5 (x6 + 4)4 D. f' (x) = 30x6 (x6 + 4) 4 4. Find the derivative of the given equationf (x) = x3 + x2 + 3 A. f'(x) = 3x2 + 2x C. f' (x) = 3x+2x+3 B. f' (x) = 3x + 2x D. f' (x ) = x3 +x2 5. Which of the following fits the slope of f (x) = -3x2 - 6x at x=1. A. 0 B. -12 C. 12 D. none 6 Find the derivative of y = 2x2 (3x - 4) A. y' = 6x3 - 8x2 C. y' = 18x2 - 16x B. y' = 15x2 - 6x D. y' = 6x - 4 7 Find the derivative of y = 5 A. 5 B. 0 C. -5 D. DNE 8 Given the function y = 3x2-5x 2x , choose which rule will be more efficient and faster. . Only the Chain Rule C. The quotient & the Chain Rules B. Only the power rule D. Product & Quotient Rules 9 Which of the following is CORRECT? A . " (-5 ) = -5 B. dx(4) = -4 "(x) =1 D. dx(V2) = 0 10. f (x) = 4x3 - 3x2 + V2x , find its derivative. A. f'(x) = 12 - 6x C. f'(x) = 12x2 - 6x + 2 B. f(x) = 12x2 - 6x + 2 D. f'(x) = 3x4 - 2x3 + x 11. SHORT ANSWERS . Use the table on the right to evaluate the first derivative of the function. x f (x) f' (x) 8(x) 8'(x) 1. 3f (4) - 2g(3) 2. 9(3) 1 2 2 f (2) 2 3 NW 3 4 4 4 5 0 5 4 -1 3 -2