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AP Calculus Basic Derivatives Flashcards | StudBud
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AP Calculus Basic Derivatives
AP Calculus Basic Derivatives
14 terms
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Power Rule and Graphs of Derivatives
Flashcards
14 cards
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Practice quiz
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Questions
14
Answers
1
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x-2
f ' (x) = -7x
f ' (x) = -7x-1
f ' (x) = 7x-2
2
If you're running in a race and you pass the person in second place, what place are you in?
Forth place
First place
Third place
Second place
3
Determine the total number of balls that would make up the figure shown.
32
24
28
30
4
What is the value of the square in the picture shown?
5
8
7
2
5
Differentiate y=\sqrt{3x+1}
y'=\frac{3}{2}\left(3x+1\right)^{-\frac{1}{2}}
y'=(3x+1)1/2
y'=\frac{3}{2}\left(3x+1\right)
y'=\frac{1}{2}\left(3x+1\right)
6
Let f (x) = x
4
+ 3x + 6. What is the instantaneous rate of change of f at x = 1?
3
7
4
10
7
Let f (x) = 6x
1/2
. What is the instantaneous rate of change at x = 4?
6
3/2
3
3/4
8
Differentiate y=5\left(x-1\right)^2 using the chain rule.
\frac{dy}{dx}=5\left(x-1\right)^2
\frac{dy}{dx}=10\left(x-1\right)^2
\frac{dy}{dx}=\left(x-1\right)
\frac{dy}{dx}=10\left(x-1\right)
9
Differentiate using correct notation y= x
4
+ x
3
+ x
2
+ x +1
dy/dx= 4x3 + 3x2 + 2x+ 2
dy/dx= 4x3 + 3x2 + 2x + 1
dy/dx= 4x4 + 3x3 + 2x2 + x +1
dy/dx= x4 + x3 + x2 + x +1
10
Differentiate using chain rule y=(2x-3)
2
dy/dx = 8x-12
dy/dx = 4x
dy/dx = 8x
dy/dx = 4x2 -12x+9
11
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 2x-1/2
f ' (x) = 2x1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 8x-1/2
12
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x2 + 5
f ' (x) = 12x3 + 5x
f ' (x) = 4x3
f ' (x) = 4x3 + 5
13
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
24
-24
-16
16
14
What is heavier: 100kg of gold or 100kg of feathers?
They are the same
Gold
Feathers
What if the scale is incorrect?
