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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