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Calculus Derivatives
Calculus Derivatives
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Questions
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Answers
1
What rule should be used in deriving f(x) = x
5
Constant rule
Sum rule
Power rule
Difference rule
2
Differentiate
y' = -24x-1
y' = 24x-1
y' = 6x-3
y' = -24x-3
3
The position function s(t)=7t
2
-18t-7 is given. What is the velocity function?
v(t)=18t-14
v(t)=14t-18
v(t)=14t+18
v(t)=18t+14
4
Find the derivative of the given equationf(x) = x
3
+ x
2
+ 3
3x + 2x
3x + 2x + 3
x3 + x2
3x2 + 2x
5
Find the derivative of the given equationf(x) = x
3
+ x
2
+ 3
f'(x) = 3x2 + 2x
f'(x) = x3 + x2
f'(x) = 3x + 2x + 3
f'(x) = 3x + 2x
6
Find the derivative of the given functionf(x) = 1/x
2
f'(x) = 2x
f'(x) = -2x
f'(x) = 1/2x
f'(x) = -2/x3
7
Find the derivative of the given equation f(x)=12-8x
12 - 8
-8
-8s
-8x
8
What is the derivative of y = 2π?
2
0
None of the above
-2
9
Find the derivative of the given equationf(x) = -4x
x
0
-4
4
10
Find the fully simplified derivative of y = 4x
2
+ 3x + 6x
-2
y' = 8x + 3 + 12/x
y' = 8x + 3 -12x-3
y' = 8x + 3 -12/x3
y' = 8x + 3 +12/x3
11
Differentiate
B
D
C
A
12
What is the derivative of f(x) = 2x
3
- 4x + 5?
f'(x) = 6x2 - 4
f'(x) = 6x2 - 4x
f'(x) = 2/3x2 - 4x
f'(x) = 3x2 - 4
13
When we "take the derivative" of a function what are we finding?
The rate at which our struggles in Calculus are increasing.
The slope of the tangent line
The slope of the secant line
What's a derivative?
14
Which function has the derivative of g'(x) = 4x
3
+ 2x - 1
g(x) = 2x4 + 2x2 - 1
g(x) = 2x3 + x3 - 2x
g(x) = x5 + x2 - x
g(x) = x4 + x2 - x
15
The derivative of a constant is equal to 1
False
True
16
Find the derivative of the given equationf(x) = 7
f'(x) = 0
f'(x) = 14
f'(x) = 7x
f'(x) = 7
17
Find the derivative of the given functionf(x) = x
4
+ 4x
3
- 2x
2
f'(x) = x3 + x2 - x
f'(x) = 4x + 12x - 4x
f'(x) = 4x3 + 12x2 + 4x
f'(x) = 4x3 + 12x2 - 4x
18
The derivative of a function is its
Instantaneous rate of change
y-intercept
Common Denominator
Maximum/Minimum
19
Find the derivative of the given equationf(x) = x
4
x4
4x
x3
4x3
20
Differentiate f(x) =(2/x
5
) - 5.
f'(x) = -10x6
f'(x) = x5-3
f'(x) = x5-5
f'(x) = -10/x6
21
Derivative means the same thing as
potato
exponent
slope of the tangent line
slope of the normal line
22
What is the derivative of x
n
?
(n+1)xn-1
(n-1)xn
nxn+1
nxn-1
23
Find the derivative of the given functionf(x) = 1 - x
2
f'(x) = -1
f'(x) = 1 - 2x
f'(x) = -2
f'(x) = -2x
24
Find dy/dx for y = 4x
3
+ 3x + 1
dy/dx = 4x2 + 3x
dy/dx = 4x2 + 3
dy/dx = 12x2 + 3
dy/dx = 12x2 + 3x
25
Find the derivative of the given equationf(x) = 1 - x
2
-2x
1 - 2x
-1
-2
