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Math Problems
Algebra 2
Csc, sec, and cot of special angles
x
6
x
8
=
□
\dfrac{x^{6}}{x^{8}}=\Box
x
8
x
6
=
□
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x
6
x
8
=
□
\dfrac{x^{6}}{x^{8}}=\Box
x
8
x
6
=
□
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y
−
4
⋅
y
3
=
□
y^{-4}\cdot y^{3}=\Box
y
−
4
⋅
y
3
=
□
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Given the function
y
=
(
2
x
−
1
)
4
y=(2 x-1)^{4}
y
=
(
2
x
−
1
)
4
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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Given the function
y
=
(
−
5
x
−
9
)
4
y=(-5 x-9)^{4}
y
=
(
−
5
x
−
9
)
4
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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Given the function
f
(
x
)
=
1
+
2
x
3
5
−
2
x
3
f(x)=\frac{1+2 x^{3}}{5-2 x^{3}}
f
(
x
)
=
5
−
2
x
3
1
+
2
x
3
, find
f
′
(
x
)
f^{\prime}(x)
f
′
(
x
)
in simplified form.
\newline
Answer:
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
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Simplify
e
ln
5
+
ln
8
e^{\ln 5+\ln 8}
e
l
n
5
+
l
n
8
and write without any logarithms.
\newline
Answer:
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Given the function
y
=
(
−
10
x
3
+
5
)
(
−
4
+
10
x
2
+
x
3
)
y=\left(-10 x^{3}+5\right)\left(-4+10 x^{2}+x^{3}\right)
y
=
(
−
10
x
3
+
5
)
(
−
4
+
10
x
2
+
x
3
)
, find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
in any form.
\newline
Answer:
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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Simplify
e
ln
10
−
ln
8
e^{\ln 10-\ln 8}
e
l
n
10
−
l
n
8
and write without any logarithms.
\newline
Answer:
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Simplify
e
ln
6
−
ln
3
e^{\ln 6-\ln 3}
e
l
n
6
−
l
n
3
and write without any logarithms.
\newline
Answer:
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d
d
x
(
x
3
4
)
=
\frac{d}{d x}\left(x^{\frac{3}{4}}\right)=
d
x
d
(
x
4
3
)
=
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y
=
x
13
y=x^{13}
y
=
x
13
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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y
=
x
10
y=x^{10}
y
=
x
10
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
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d
d
x
(
x
2
3
)
=
\frac{d}{d x}\left(x^{\frac{2}{3}}\right)=
d
x
d
(
x
3
2
)
=
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d
d
x
[
x
6
]
=
\frac{d}{d x}\left[x^{6}\right]=
d
x
d
[
x
6
]
=
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d
d
x
[
x
3
]
=
\frac{d}{d x}\left[x^{3}\right]=
d
x
d
[
x
3
]
=
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d
d
x
[
x
9
]
=
\frac{d}{d x}\left[x^{9}\right]=
d
x
d
[
x
9
]
=
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d
d
x
(
x
2
−
x
+
5
4
x
−
1
)
=
\frac{d}{d x}\left(\frac{x^{2}-x+5}{4 x-1}\right)=
d
x
d
(
4
x
−
1
x
2
−
x
+
5
)
=
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d
d
x
(
2
x
2
+
x
−
3
2
x
+
7
)
=
\frac{d}{d x}\left(\frac{2 x^{2}+x-3}{2 x+7}\right)=
d
x
d
(
2
x
+
7
2
x
2
+
x
−
3
)
=
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d
d
x
(
3
x
2
−
1
x
−
2
)
=
\frac{d}{d x}\left(\frac{3 x^{2}-1}{x-2}\right)=
d
x
d
(
x
−
2
3
x
2
−
1
)
=
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Evaluate. Write your answer as a whole number or as a simplified fraction.
\newline
5
6
5
4
=
\frac{5^{6}}{5^{4}}=
5
4
5
6
=
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Evaluate. Write your answer in simplified, rationalized form. Do not round.
\newline
csc
6
0
∘
=
\csc 60^\circ =
csc
6
0
∘
=
______
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