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Calculus Basic Derivatives (2.2) Flashcards | StudBud
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Calculus Basic Derivatives (2.2)
Calculus Basic Derivatives (2.2)
12 terms
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Power Rule and Graphs of Derivatives
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Questions
12
Answers
1
Find the derivative
f'(x) = (1/2)x - (-1/2)x
f'(x) = 1/(2x1/2) - 1/(2x3/2)
f'(x) = 1/(2x)1/2 + 1/(2x)3/2
f'(x) = 1/(2x1/2) + 1/(2x3/2)
2
Find the derivative
f'(x) = 2 - 4/x2
y' = (6x2 - 6x + 4)/(2x)
f'(x) = 2x - 3 + 4/x
f'(x) = 3x - 3 + 2/x
3
Find the derivative
f'(t) = 3sin(t) + (1/4)cos(t)
f'(t) = -3cos(t) + (1/4)sin(t)
f'(t) = 3cos(t) - (1/4)sin(t)
f'(t) = -3sin(t) - (1/4)cos(t)
4
Let f (x) = -2x
3
+ x
2
- 4x. What is the slope of the tangent line at x = 2 ?
16
24
-24
-16
5
Let f (x) = x
4
+ 3x + 6. What is the slope of the tangent line at x = 1?
4
10
3
7
6
Find the derivative of f(x) = 4x
1/
2
+ 2
f ' (x) = 8x-1/2
f ' (x) = 8x-1/2 + 2
f ' (x) = 2x-1/2
f ' (x) = 2x1/2
7
Given f (x) = x
4
+ x
3
- x + 1, what is f ' (1) ?
2
6
8
7
8
Let f (x) = 6x
1/2
. What is the slope of the tangent line at x = 4?
6
3
3/2
3/4
9
Let f (x) = 5x
2
. Find an equation of the tangent line to f(x) at x = 2.
y = 20x - 20
y = 20x - 40
y = 20x - 10
y = 10x - 20
10
Find the derivative g(t) = 2/(3t
2
)
f'(t) = (-4/3)t3
f'(t) = (4/3)t
f'(t) = -4/(3t3)
f'(t) = 4/(3t3)
11
Find the derivative of f(x) = x
4
+ 5x
f ' (x) = 4x3
f ' (x) = 12x3 + 5x
f ' (x) = 4x3 + 5
f ' (x) = 4x2 + 5
12
Find the derivative of f(x) = 7x
-1
f ' (x) = -7x-2
f ' (x) = -7x-1
f ' (x) = -7x
f ' (x) = 7x-2
