Calculus
2.5 Worksheet #2
Name:____________________________________
Mitchell
o Show your work whenever possible and circle your final answers.
1) If f(x) = (x2 − 3x) 2 , then f '(4) =
3
A.
B.
C.
D.
E.
2)
15/2
9
21/2
15
33/2
(
)
d
sec2 ( x ) =
dx
2sec2 ( x )tan( x )
B.
x
2
sec ( x )tan( x )
E.
2 x
2sec( x )tan( x )
A.
x
sec( x )tan( x )
D.
x
3)
d 2
( x cos(2x)) =
dx
A. −2xsin(2x)
B. 2x ( − xsin(2x) + cos(2x) )
C. 2x ( xsin(2x) − cos(2x))
(
D. 2x x2 sin(2x) + cos(2x)
)
4) Which of the following is y’ if y = cos2 (x 3 + x2 ) ?
A. −(3x2 + 2x)cos(x3 + x2 )sin(x3 + x2 )
B. −2(3x2 + 2x)cos(3x2 + 2x)sin(3x2 + 2x)
C. −2(3x2 + 2x)cos(x 3 + x2 )sin(x 3 + x2 )
D. 2(3x2 + 2x)cos(x 3 + x2 )sin(x3 + x2 )
5) Find the second derivative of f(x) if f(x) = 4sin2 (3x) .
A. 24cos2 (3x) + 24sin2 (3x)
B. 24cos2 (3x) − 24sin2 (3x)
C. −72cos(3x)sin(3x)
D. 72cos2 (3x) + 72sin2 (3x)
E. 72cos2 (3x) − 72sin2 (3x)
sec2 ( x )tan( x )
C.
x
6) If y = 4 −4x5 + 3 , then dy/dx =
1
A.
3
4
20x 4
B. −
4
20
C. −
4 4 ( −4x + 3)
5
( −4x5 + 3)3
5x 4
D. −
( −4x5 + 3)3
4
( −4x5 + 3)3
7) Find f '(x) if f(x) = ( −4x − 1)2 ( − x5 + 4)5 .
A. f '(x) = 400x 4 ( − x 5 + 4)4 ( −4x − 1)
B. f '(x) = ( −4x − 1)( − x 5 + 4)4 (108x5 + 25x 4 − 32)
C. f '(x) = 32x + 8 − 25x 4 ( − x 5 + 4)4
D. f '(x) = −25x 4 ( −4x − 1)2 ( − x5 + 4)4
8) If f(x) = cot(2x 4 + 3)2 , find f '(x) .
A. f '(x) = −16x 3 csc2 (2x 4 + 3)2 (2x 4 + 3)
B. f '(x) = −16x3 sin2 (2x 4 + 3)2 (2x 4 + 3)
C. f '(x) = 16x 3 csc2 (2x 4 + 3)2 (2x 4 + 3)
D. f '(x) = −16x 3 cos2 (2x 4 + 3)2 (2x 4 + 3)
9) If y = (2x3 + 5)tan(x 5 ) , find dy/dx.
A.
dy
dx
B.
dy
dx
dy
dx
dy
dx
C.
D.
10)
= x2 ( 5x2 sec2 (x 5 ) + 6 )
= 6x2 tan(x5 ) + 5x 4 (2x 3 + 5)sec2 (x 5 )
= 6x2 tan(x5 )
= 60x 6 sec2 (x 5 )
(
)
d
sec3 3x2 − 1 =
dx
( 3x − 1) tan( 3x − 1)
9xsec ( 3x − 1) tan ( 3x − 1)
A. 9x 3x2 − 1isec2
2
B.
2
3x2 − 1
2
2
9xsec3
C.
2
3sec2
D.
(
(
) (
3x2 − 1 tan
3x2 − 1
) (
3x2 − 1 tan
2 3x2 − 1
)
3x2 − 1
)
3x2 − 1