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Kazeer [188]
3 years ago
7

Use the Quotient Rule to find the UNSIMPLIFIED version of the derivative. R(w)=3w+w^4/ 2w^2+1.

Mathematics
1 answer:
PolarNik [594]3 years ago
6 0

From your previous questions, you know

(3<em>w</em> + <em>w</em>⁴)' = 3 + 4<em>w</em>³

(2<em>w</em>² + 1)' = 4<em>w</em>

So by the quotient rule,

<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3<em>w</em> + <em>w</em>⁴)' - (3<em>w</em> + <em>w</em>⁴)•(2<em>w</em>² + 1)' ] / (2<em>w</em>² + 1)²

That is, the quotient rule gives

<em>R'(w)</em> = [ (denominator)•(derivative of numerator) - (numerator)•(derivative of denominator) ] / (denominator)²

I'm not entirely sure what is meant by "unsimplified". Technically, you could stop here. But since you already know the component derivatives, might as well put them to use:

<em>R'(w)</em> = [ (2<em>w</em>² + 1)•(3 + 4<em>w</em>³) - (3<em>w</em> + <em>w</em>⁴)•(4<em>w</em>) ] / (2<em>w</em>² + 1)²

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It is a solid shape that contains lateral surface and two circular bases which are parallel and congruent.
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B (cylinder)

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Two <u>circular</u> bases which are parallel and congruent :

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The cube doesn't have any circular bases.

The sphere doesn't have any faces, nor edges.

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A cylinder has two circular bases, as well as they are parallel and congruent.

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8 0
2 years ago
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F U    C K  BRAINLY

7 0
3 years ago
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Find the volume of cylinder<br> Diameter of base is 11 cm<br> Height of cylinder is 16cm
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1520.5 cm³

Step-by-step explanation:

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3 0
3 years ago
(8x^3 - x) - (10x - 5x^2 - 3x^3) <br> Show your work.
sergeinik [125]

Let's simplify step-by-step.
8
x
3
−
x
−
(
10
x
−
5
x
2
−
3
x
3
)
Distribute the Negative Sign:
=
8
x
3
−
x
+
−
1
(
10
x
−
5
x
2
−
3
x
3
)
=
8
x
3
+
−
x
+
−
1
(
10
x
)
+
−
1
(
−
5
x
2
)
+
−
1
(
−
3
x
3
)
=
8
x
3
+
−
x
+
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10
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5
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+
3
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Combine Like Terms:
=
8
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3
+
−
x
+
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10
x
+
5
x
2
+
3
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=
(
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5
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=
11
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5
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Answer:
=
11
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11
x


Brainliest Please:)
6 0
3 years ago
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