NEW
Font size
S
M
L
XL
WorksheetsCalculus Velocity and Derivatives
Total questions: 25
Worksheet time: 1hrs 6mins
Name
Class
Date
1.
Find the derivative of f(x)=(x3-2x)2
a)
6x5 - 12x3+8x
b)
6x5 - 16x3+8x
c)
x6-4x4+4x2
d)
6x5 - 16x3-8x
2.
Determine the derivative:
a)
A
b)
B
c)
C
d)
D
3.
Find dy/dx for
y = 32x+5
y = 32x+5
a)
dy/dx = 3(2x+4)
b)
dy/dx = (3(2x+4)) ln 3
c)
dy/dx = 3(2x+5) ln3
d)
dy/dx = (3(2x+5)) (ln 3) (2)
4.
a)
A
b)
B
c)
C
d)
D
5.
Find dy/dx for y=-(3x2+5x)5
a)
y=-5(x+5)4
b)
y=-5(6x+5)(3x2+5x)4
c)
y=-6x+5(3x2+5x)4
d)
y=-6x(3x2+5x)4
6.
Differentiate:
f(x) = x3e4x
*You will need to remove the Greatest Common Factor
f(x) = x3e4x
*You will need to remove the Greatest Common Factor
a)
f '(x) = 3x2e4x
b)
f '(x) = 3x2e4x+3x2e4x
c)
f '(x) = x2e4x(4x+3)
d)
f '(x) = xe4x(4x2+3x)
7.
Differentiate y = √(x² - 1)
a)
√(x² -1)
b)
(1/2x)(x² - 1)^(-1/2)
c)
x(x² - 1)^(-1/2)
d)
x(x² - 1)^(1/2)
8.
d/dx (sin2x) = ?
a)
2sin x
b)
2(sin x)(cos x)
c)
2cos x
d)
2x(cos x)
9.
Find the derivative:
y=4ex²
y=4ex²
a)
y'=8xe
b)
y'=8xex²
c)
y'=8xe2x
d)
y'=8xe4x²
10.
Find the derivative:
y=5x2e3x
y=5x2e3x
a)
y'=10xe3x(2x+3)
b)
y'=5xe3x(3x+2)
c)
y'=10ex3x(3x+2)
d)
y'=5xe3x(2x+3)
11.
Find the derivative:
y=11x²
y=11x²
a)
y′=11x²(2x)(ln11)
b)
y′=2x(ln11)
c)
y′=11x²(2x)(lnx)
d)
y′=11x²(x)(ln11)
12.
.
a)
(3x^2-2)cos(x^3-2x)
b)
-(3x^2-2)cos(x^3-2x)
c)
cos(2x^2-2)
d)
sin(2x^2-2)
13.
Find the derivative of f(x) = x2sinx
a)
f'(x) = 2xsinx - x2cosx
b)
f'(x) = 2xsinx + x2sinx
c)
f'(x) = 2xsinx + x2cosx
d)
f'(x) = 2xcosx
14.
Find the derivative f(x) = tanxcosx
a)
f'(x) = sec2xcosx - tanxsinx
b)
f'(x) = sec2xcosx + tanxsinx
c)
f'(x) = sec2xsinx
d)
f'(x) = sec2xcosx - tanxcosx
15.
What is f'(x) if f(x) = cos(5x4)?
a)
f'(x) = sin(20x3)
b)
f'(x) = 20x3 sin(5x4)
c)
f'(x) = -sin(20x3)
d)
f'(x) = -20x3 sin(5x4)
16.
The equation of the tangent to y=1/x at x=3 is
a)
y=-1/9x+2/3
b)
y=1/3x+1/3
c)
y=1/9x+9
d)
y=1/9x
17.
The position function x(t)=t3+6t2+16t-18 is given on the interval of 0<x<9. What is the velocity at t=6?
a)
197
b)
190
c)
18
d)
196
18.
Find the derivative of g(x)=(3x-2)/(x2+2)
a)
9x2+2
b)
3(x2+2)/(x2+2)2
c)
(-3x2+4x +6)/(x2+2)2
d)
(-3x2+10)/(x2+2)2
19.
Find the second derivative of f(x) = x2 + ex - cosx
a)
f"(x) = 2 + ex + cosx
b)
f"(x) = 2x + ex + cosx
c)
f"(x) = 2x + xex - cosx
d)
f"(x) = 2x + ex + sinx
20.
Find dy/dx
a)
A
b)
B
c)
C
d)
D
21.
a)
1/(3x2+5)1/4
b)
(3x)/(2(3x2+5))
c)
(2(3x2+5)3/4)/(3x)
d)
(3x2+5)1/4
22.
a)
(5(1-4x))/(12x3)
b)
5(x+1)(3x3-4x2+4x-4)
c)
(5(x3+16))/(x(x3+4))
d)
(5(x+1)(-3x3+4x2-4x+4))/(3x4(x3+4))
23.
a)
((3x2-5)(x2+1))/(10x2(3x4-5))
b)
(2(-3x4-5))/(5x(3x4-5))
c)
(3x2-1)/(60x3)
d)
((3x2-5)(-x2-1))/5
24.
a)
1/(cos(5x2))
b)
-(10xsin(5x2))/(cos(5x2))
c)
-1/(10xsin(5x2))
d)
cos(5x2)
25.
a)
1/(2x5)
b)
1/(10x4)
c)
2x5
d)
5/x
Reset
