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WorksheetsCalculus Derivative Practice
Total questions: 36
Worksheet time: 52mins
Name
Class
Date
1.
What is the derivative?
a)
A
b)
B
c)
C
d)
D
2.
What is the derivative of sin(x)?
a)
sin(x)
b)
cos(x)
c)
-sin(x)
d)
-cos(x)
3.
If a function has a derivative that is negative, what does that tell you?
a)
The function is increasing
b)
The function is decreasing
4.
What is the derivative of cos(x)?
a)
sin(x)
b)
cos(x)
c)
-sin(x)
d)
-cos(x)
5.
a)
cosx
b)
-cosx
c)
-sinx cosx
d)
sinx cosx
6.
a)
sinx
b)
-sinx
c)
-cscx cotx
d)
sec2x
7.
sin π/4
a)
√2∕2
b)
1/2
c)
√3/2
d)
0
8.
sec 3π/2
a)
0
b)
undefined
c)
1
d)
-1
9.
a)
cos x
b)
csc x
c)
sec x
d)
cot x
10.
cos 4π/3
a)
-√3/2
b)
√3/2
c)
1/2
d)
-1/2
11.
a)
csc x
b)
sec x
c)
cot x
d)
tan x
12.
a)
csc x
b)
sec x
c)
cot x
d)
tan x
13.
Find the derivative of the given equation
f(x) = 7
f(x) = 7
a)
7
b)
0
c)
7x
d)
14
14.
Find the derivative of the given equation
f(x) = -4x
f(x) = -4x
a)
4
b)
x
c)
-4
d)
0
15.
Find the derivative of the given equation
g(x) = 6 + ⅔x
g(x) = 6 + ⅔x
a)
6
b)
12
c)
6 + ⅔
d)
⅔
16.
Find the derivative of the given equation
f(x) = 1 - x2
f(x) = 1 - x2
a)
1 - 2x
b)
-2x
c)
-2
d)
-1
17.
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
18.
Solve f '(2) for
f(x) = x2 + 2x
f(x) = x2 + 2x
a)
2x + 2
b)
6
c)
12
d)
2x
19.
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
20.
Differentiate f(x) =(2/ x5) - 5.
a)
x5-3
b)
-10x6
c)
x5-5
d)
-10x-6
21.
Differentiate f(x) = 5x7.
a)
35x6
b)
210x5
c)
5x6
d)
1050x4
22.
Derive y=3x2-4x+2
a)
6x-6
b)
6x-2
c)
4-6x
d)
6x-4
23.
Where is the graph not differentiable?
a)
x = -2, -1, 0, 1
b)
x = -2, -1, 1
c)
x = -2, -1
d)
x = -1,
24.
The derivative of a function is its
a)
Slope
b)
Maximum/Minimum
c)
Instantaneous rate of change
d)
Common Denominator
25.
f' is given, which could be f?
a)
A
b)
B
c)
C
26.
Where is the graph neither continuous nor differentiable?
a)
x = -1, 0, 1, 2
b)
x = -1, 1
c)
x = -1, 0, 1
d)
x = -1, 0, 2
27.
Derivative means the same thing as
a)
slope of the tangent line
b)
slope of the normal line
c)
actual height
d)
intended height
28.
What is the limit?
a)
5/2
b)
-2/3
c)
Infinity
d)
17/3
29.
What is the limit?
a)
Infinity
b)
20
c)
DNE
d)
12
30.
What is the derivative of sec(x)?
a)
sec(x)tan(x)
b)
csc(x)cot(x)
c)
-sec(x)tan(x)
d)
-csc(x)cot(x)
31.
Find the derivative.
a)
x4 cosx - 4x3sinx
b)
x4 cosx + 4x3sinx
c)
4x3cosx
d)
-4x3cosx
32.
What is the derivative of tan(x)?
a)
-sec2(x)
b)
-csc2(x)
c)
sec2(x)
d)
csc2(x)
33.
Which if the following is not a correct notation for 'derivative?'
a)
f'(x)
b)
y'
c)
dy
d)
dy/dx
34.
How many derivatives can you take of a function?
a)
only 3
b)
only 2
c)
only 1
d)
until you can no longer derive it
35.
The derivative of
a)
y'=2x-x-2
b)
y'=x-1+8x
c)
y'=x-2+8x
d)
y=8x-x-2
36.
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
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