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AP Application Worksheet-Derivatives #1 : Chain rule and trigonometric functions 1. If f(x) = sin²(3-x), then f ’(0) = A) -2cos 3 B)-2sin 3 cos 3 C) 6 cos 3 D) 2sin 3 cos 3 E)6 sin 3 cos 3 C) 2(3x² + 1) D) 3x²(x³ + 1) E) 6x²(x³ + 1) 2. If y = (x³ + 1)², then A) (3x²)² B) 2(x³ + 1) 3. If y = x²sin 2x, then A) 2xcos 2x B) 4x cos 2x C) 2x(sin 2x + cos 2x) D) 2x(sin 2x – x cos 2x) E)2x(sin 2x + x cos 2x) 4. If f(x) = cos (3x), then f ‘ ( A) = B) 5. If f(x) = x C) D) E) , then f ’(x) = A) B) C) D) E) 6. cos²(x³) = A) B) C) D) E) 6x²sin (x³) cos (x³) 6x² cos (x³) sin²(x³) – 6x² sin(x³)cos(x³) – 2 sin(x³)cos(x³) 7. The line normal to the curve y = A) 8 B) 4 at the point (0, 4) has slope C) D) E) 8