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WorksheetsQuiz #3 STEM - Basic Calculus
Total questions: 30
Worksheet time: 1hrs 13mins
Name
Class
Date
1.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
slope of the secant line
d)
the function’s value
2.
When we "take the derivative" of a function what are we finding?
a)
What's a derivative?
b)
The rate at which our struggles in Calculus are increasing.
c)
The slope of the secant line
d)
The slope of the tangent line
3.
What is the derivative of xn?
a)
(n-1)xn
b)
nxn+1
c)
(n+1)xn-1
d)
nxn-1
4.
What is the derivative of f(x)= cx?
a)
c
b)
x
c)
1
d)
0
5.
Differentiate y= x3 + 2x
a)
3x3+2x
b)
3x2+2
c)
3x+2
d)
3x
6.
Find the derivative of the given equation
f(x) = x4 + 4x3 - 2x2
f(x) = x4 + 4x3 - 2x2
a)
x3 + x2 - x
b)
4x3 + 12x2 + 4x
c)
4x + 12x - 4x
d)
4x3 + 12x2 - 4x
7.
Find the derivative of the given equation
f(x) = 1/x2
f(x) = 1/x2
a)
1/2x
b)
-2x
c)
2x
d)
-2x-3
8.
Set up the derivative of y=(3x4 - 7)*(5x2 + 1)
a)
(12x3)*(10x)
b)
(3x4 - 7)*(10x) + (12x3)*(5x2 + 1)
c)
(3x4 - 7)*(10x) - (12x3)*(5x2 + 1)
d)
(3x4 - 7)/(10x) + (12x3)/(5x2 + 1)
9.
Find the derivative of y = 2x2 (3x - 4)
a)
6x3 - 8x2
b)
18x2 - 16x
c)
15x2 - 6x
d)
6x - 4
10.
Differentiate f(x) =(2/ x5) - 5.
a)
x5-3
b)
-10x6
c)
x5-5
d)
-10x-6
11.
Find the derivative f(x) = xex
a)
f'(x) = ex
b)
f'(x) = xex + xex
c)
f'(x) = ex - xex
d)
f'(x) = ex + xex
12.
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
13.
Find the derivative.
f(x) = -8x-3 + 5x - ex
f(x) = -8x-3 + 5x - ex
a)
f'(x) = -24x-4 + 5 - ex
b)
f'(x) = 24x-4 + 5 - ex
c)
f'(x) = 24x-2 + 5 - ex
d)
f'(x) = 24x-4 + 5 - ex-1
14.
Find y' if y=e3x
a)
e3x
b)
e2x
c)
0
d)
3e3x
15.
Find the derivative of the given equation
f(x) = 7
f(x) = 7
a)
7
b)
0
c)
7x
d)
14
16.
Find the derivative of the given equation
f(x) = -4x
f(x) = -4x
a)
4
b)
x
c)
-4
d)
0
17.
Find the derivative of the given equation
f(x) = 1 - x2
f(x) = 1 - x2
a)
1 - 2x
b)
-2x
c)
-2
d)
-1
18.
Determine the derivative of: f(x) = x4sinx
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
19.
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
20.
What is the derivative of -cos(x)?
a)
sin(x)
b)
-sin(x)
c)
cos(x)
d)
-cos(x)
21.
If f(x) = sin3(2x), then f'(x) =
a)
3cos(2x)
b)
3sin(2x)⋅2
c)
3sin2(2x)cos(2x)
d)
3sin2(2x)cos(2x)⋅2
22.
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)
23.
Find g'(x) if g(x) = sin1/2(4x)
a)
2cos-1/2(4x)
b)
4cos1/2(4x)
c)
2sin-1/2(4x)cos(4x)
d)
1/2sin-1/2(4x)cos(4x)
24.
.
a)
(3x2-2)cos(x3-2x)
b)
-(3x2-2)cos(x3-2x)
c)
cos(2x2-2)
d)
sin(2x2-2)
25.
y= sin2x find y'
a)
2sin x
b)
2(sin x)(cos x)
c)
2cos x
d)
2x(cos x)
26.
Find y' if
y = 10sin(x) +3cos(x)
a)
10sin(x)cos(x)+ 3cos(x)sin(x)
b)
10cos(x) - 3cos(x)
c)
30cos(x)sin(x)
d)
10cos(x) -3sin(x)
27.
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)
28.
Determine the derivative of: f(x) = x4sinx
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
29.
If f(x) = -csc(x/2), then f'(x) =
a)
sec2(x/2)
b)
2csc(x/2)cot(x/2)
c)
½csc(x/2)cot(x/2)
d)
-csc2(x/2)
30.
Find the derivative of f(x) = -3x4cscx
a)
f'(x) = 12x3cscxcotx
b)
f'(x) = -3x4cscxcotx
c)
f'(x) =-12x3cscx + 3x4cotxcscx
d)
f'(x) = -3xcosx
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