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Calculus - Derivatives Flashcards | StudBud
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Calculus - Derivatives
Calculus - Derivatives
23 terms
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Calculus
Flashcards
23 cards
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Questions
23
Answers
1
f(x)=cos(x+4)
Product
Quotient
Chain
Power
2
What happens to a constant function during differentiation?
The value of the constant will be the same
The value of the constant will be equal to 1
There can not be constants in differenciation
The value of the constant will be equal to 0
3
What is the answer to dy/dx= X
-4
?
f '(x)= -3x-5
dy/dx= -4x-5
f '(x)= -5x-4
f '(x)= -4x5
4
f(x)=2x
3
(cosx)
Product
Quotient
Chain
Power
5
What is the derivative for dy/dx=√x?
f (x)= 1/2x-1/2
f '(x)= -1/2x-1/2
f '(x)= 1/2x-1/2
f '(x)= 1/2x1/2
6
The equation of the line tangent to f(x)=x
2
+1 at (1, 2) is
y-2=2(x-1)
y+2=2(x-1)
y=2x
y-1=2(x-2)
7
What rule is not used for differentiation?
power
quotient
produce
cable
8
What is the derivative for dy/dx = 1 + 1/x ?
y = -1/(-x)2
y '= 1/x2
y '= x-2
y '= -1/x2
9
What is the derivative of f (x)= x
7
f '(x)= 2x6
dy/dx= 7x6
f (x)= 6x7
f '(x)= 6x7
10
What happens when you have Y= f(x) + g(x)?
Both f(x) and g(x) are derivated and multiplied
Only g(x) is derivated
Both f(x) and g(x) are derivated then added
Only f(x) is derivated
11
What is the derivative for dy/dx= x
3
-4x
2
?
f (x)= 3x2 -8x
f '(x)= 3x3 -8x
f '(x)= 3x2 -16x
f '(x)= 3x2 -8x
12
What is the derivative for dy/dx= x
2
+ 1/x?
y '= -1/x-2
y '= -1/x2
y = -1/x2
y '= 1/x2
13
The equation of the line tangent to f(x)=sin(3x) at (π , 0)
y-0=-3(x-π)
y=3x+3
y-π=3(x+0)
y=x+3π
14
What is the derivative for y= 3x
2
+x-3 ?
f '(x)= 6x-2 + 1
f '(x)= 6x + 3
f '(x)= 6x2 + 1
f '(x)= 6x + 1
15
What are the ways to name the derivative?
y'
instantaneous rate of change
Slope of line tangent
f '(x)
16
If f(x) = 3-2sin(x), then f '(π) =
2
1
1/2
-1
17
What is the derivative for f(x)= (x+3)
2
?
y '= 2x -6/x2
y '= 2x -7/x
y '= 2x -7/x2
y = 2x -7/x2
18
What are derivatives useful for?
To calculate the slope tangent a curve in different places
To Calculate the best fit line in a scatter graph
To find the range of a model
To calculate the mean of a set of numbers
19
What is the derivative for f(x)= x
-1
?
dy/dx= x-2
dy/dx= -x2
dy/dx= -x-2
dx/dy= -x-2
20
What is the derivative for f (x)=5x
2
?
f'(x)= 10x
y= 10x2
y '= 10x2
dx/dy = 10x
21
What is the derivative for y= 3/x
2
?
y'= 6x-3
y'= -6x-3
y'= -6x3
y= -6x-3
22
If f(x)=3x
2
e
x
, f ' (1) =
3e3
e9
9e
3
23
What is the derivative for f(x)= 2x
3
+9
dy/dx= 6x2
dy/dx= 4x2
dy/dx= 3x2
dy/dx= 6x3
