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Let’s check out your problem:
If
y
=
x
3
+
2
x
+
5
y = x^3 + 2x + 5
y
=
x
3
+
2
x
+
5
and
z
=
x
2
+
7
x
+
1
z = x^2 + 7x + 1
z
=
x
2
+
7
x
+
1
, what is
2
y
+
z
2y + z
2
y
+
z
in terms of
x
x
x
?
\newline
A)
3
x
3
+
11
x
+
11
3x^3 + 11x + 11
3
x
3
+
11
x
+
11
\newline
B)
2
x
3
+
x
2
+
9
x
+
6
2x^3 + x^2 + 9x + 6
2
x
3
+
x
2
+
9
x
+
6
\newline
C)
2
x
3
+
x
2
+
11
x
+
11
2x^3 + x^2 + 11x + 11
2
x
3
+
x
2
+
11
x
+
11
\newline
D)
2
x
3
+
2
x
2
+
18
x
+
12
2x^3 + 2x^2 + 18x + 12
2
x
3
+
2
x
2
+
18
x
+
12
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Math Problems
Calculus
Find derivatives of other trigonometric functions
Full solution
Q.
If
y
=
x
3
+
2
x
+
5
y = x^3 + 2x + 5
y
=
x
3
+
2
x
+
5
and
z
=
x
2
+
7
x
+
1
z = x^2 + 7x + 1
z
=
x
2
+
7
x
+
1
, what is
2
y
+
z
2y + z
2
y
+
z
in terms of
x
x
x
?
\newline
A)
3
x
3
+
11
x
+
11
3x^3 + 11x + 11
3
x
3
+
11
x
+
11
\newline
B)
2
x
3
+
x
2
+
9
x
+
6
2x^3 + x^2 + 9x + 6
2
x
3
+
x
2
+
9
x
+
6
\newline
C)
2
x
3
+
x
2
+
11
x
+
11
2x^3 + x^2 + 11x + 11
2
x
3
+
x
2
+
11
x
+
11
\newline
D)
2
x
3
+
2
x
2
+
18
x
+
12
2x^3 + 2x^2 + 18x + 12
2
x
3
+
2
x
2
+
18
x
+
12
Write Equations:
First, let's write down the given equations for
y
y
y
and
z
z
z
:
y
=
x
3
+
2
x
+
5
,
y = x^3 + 2x + 5,
y
=
x
3
+
2
x
+
5
,
z
=
x
2
+
7
x
+
1.
z = x^2 + 7x + 1.
z
=
x
2
+
7
x
+
1.
Now, we need to find
2
y
+
z
2y + z
2
y
+
z
.
Calculate
2
y
2y
2
y
:
Calculate
2
y
2y
2
y
:
2
y
=
2
(
x
3
+
2
x
+
5
)
=
2
x
3
+
4
x
+
10
2y = 2(x^3 + 2x + 5) = 2x^3 + 4x + 10
2
y
=
2
(
x
3
+
2
x
+
5
)
=
2
x
3
+
4
x
+
10
.
Add
2
y
2y
2
y
and
z
z
z
:
Now, add
2
y
2y
2
y
and
z
z
z
:
2
y
+
z
=
(
2
x
3
+
4
x
+
10
)
+
(
x
2
+
7
x
+
1
)
=
2
x
3
+
x
2
+
11
x
+
11.
2y + z = (2x^3 + 4x + 10) + (x^2 + 7x + 1) = 2x^3 + x^2 + 11x + 11.
2
y
+
z
=
(
2
x
3
+
4
x
+
10
)
+
(
x
2
+
7
x
+
1
)
=
2
x
3
+
x
2
+
11
x
+
11.
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Find the derivative of
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\newline
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Find the derivative of
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\newline
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Find the derivative of
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Find the derivative of
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(
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\newline
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′
(
x
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=
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=
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