Power Rule 2
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Question 1 of 5
1. Question
Find the derivativef(x)=2x-5f(x)=2x−5- (2)
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Power Rule
f′(x)=nxn−1Remember
Differentiating a constant makes it 0.First, identify the values of the functionFirst term:f(x) = xn f(x) = 2x1−5 x = 2x n = 1 Second term:f(x) = xn f(x) = 2x−5 x = 5 Substitute the values into the power ruleFirst term:f′(x) = nxn−1 = 1⋅2x1−1−5 Substitute known values = 2-5 Second term:f′(x) = nxn−1 = 2−0 Differentiating a constant makes it 0 = 2 f′(x)=2 -
Question 2 of 5
2. Question
Find the derivativef(x)=12x6- 1.
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2.
f′(x)=3x5 -
3.
f′(x)=12x5 -
4.
f′(x)=6x5
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Chapters- Chapters
Power Rule
f′(x)=nxn−1First, identify the values of the functionf(x) = xn f(x) = 12x6 x = 12x n = 6 Substitute the values into the power rulef′(x) = nxn−1 = 6⋅12x6−1 Substitute known values = 3x5 f′(x)=3x5 -
Question 3 of 5
3. Question
Find the derivativef(x)=14x5-
1.
f′(x)=-54x -
2.
f′(x)=54x6 -
3.
f′(x)=54x -
4.
f′(x)=-54x6
Hint
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Chapters- Chapters
Power Rule
f′(x)=nxn−1First, reciprocate x5 to remove the exponent from the denominatorf(x) = 14x5 = 14x-5 Reciprocate x5 Next, identify the values of the functionf(x) = xn f(x) = 14x−5 x = 14x n = -5 Substitute the values into the power rulef′(x) = nxn−1 = −5⋅14x−5−1 Substitute known values = -54x-6 = -54x6 Reciprocate x-6 f′(x)=-54x6 -
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Question 4 of 5
4. Question
Find the derivativef(x)=23x3-
1.
f′(x)=-2x3 -
2.
f′(x)=12x4 -
3.
f′(x)=2x4 -
4.
f′(x)=-2x4
Hint
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Chapters- Chapters
Power Rule
f′(x)=nxn−1First, reciprocate x3 to remove the exponent from the denominatorf(x) = 23x3 = 23x-3 Reciprocate x5 Next, identify the values of the functionf(x) = xn f(x) = 23x−3 x = 23x n = -3 Substitute the values into the power rulef′(x) = nxn−1 = −3⋅23x−3−1 Substitute known values = -2x-4 = -2x4 Reciprocate x-4 f′(x)=-2x4 -
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Question 5 of 5
5. Question
Find the derivativef(x)=3x4-
1.
f′(x)=-4x5 -
2.
f′(x)=-12x5 -
3.
f′(x)=12x5 -
4.
f′(x)=-12x4
Hint
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Correct!
Incorrect
Need TextPlayCurrent Time 0:00/Duration Time 0:00Remaining Time -0:00Stream TypeLIVELoaded: 0%Progress: 0%0:00Fullscreen00:00MutePlayback Rate1x- 2x
- 1.5x
- 1.25x
- 1x
- 0.75x
- 0.5x
Subtitles- subtitles off
Captions- captions off
- English
Chapters- Chapters
Power Rule
f′(x)=nxn−1First, reciprocate x4 to remove the exponent from the denominatorf(x) = 3x4 = 3x-4 Reciprocate x32 Next, identify the values of the functionf(x) = xn f(x) = 3x−4 x = 3x n = -4 Substitute the values into the power rulef′(x) = nxn−1 = −4⋅3x−4−1 Substitute known values = -12x-5 = -12x5 Reciprocate x-5 f′(x)=-12x5 -
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