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Math Problems
Calculus
Find derivatives using the chain rule I
∑
n
=
1
3
(
n
−
1
)
=
\sum_{n=1}^{3}(n-1)=
∑
n
=
1
3
(
n
−
1
)
=
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∑
x
=
1
3
(
4
x
)
=
\sum_{x=1}^{3}(4 x)=
∑
x
=
1
3
(
4
x
)
=
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∑
k
=
0
1
(
2
k
−
1
)
=
\sum_{k=0}^{1}(2 k-1)=
∑
k
=
0
1
(
2
k
−
1
)
=
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∑
j
=
1
3
(
3
j
)
=
\sum_{j=1}^{3}(3 j)=
∑
j
=
1
3
(
3
j
)
=
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Polynomial function
g
g
g
is defined as
g
(
x
)
=
x
3
−
a
x
2
−
17
x
+
12
g(x)=x^{3}-a x^{2}-17 x+12
g
(
x
)
=
x
3
−
a
x
2
−
17
x
+
12
, where
a
a
a
is a constant. If
x
+
4
x+4
x
+
4
is a factor of the polynomial, then what is the value of
a
a
a
?
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Solve the following equation for
x
x
x
.
\newline
x
2
−
x
−
2
=
x
−
2
x
=
□
\begin{array}{l} \sqrt{x^{2}-x-2}=x-2 \\ x=\square \end{array}
x
2
−
x
−
2
=
x
−
2
x
=
□
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The equation
2
c
⋅
b
c
=
1
0
c
2^{c} \cdot b^{c}=10^{c}
2
c
⋅
b
c
=
1
0
c
is true for all values of
c
c
c
. What is the value of
b
b
b
?
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If
3
a
=
3
4
5
3^{a}=\sqrt[5]{3^{4}}
3
a
=
5
3
4
, what is the value of
a
a
a
?
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If
3
a
=
3
2
5
3^{a}=\sqrt[5]{3^{2}}
3
a
=
5
3
2
, what is the value of
a
a
a
?
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The equation
(
x
3
+
y
)
⋅
x
5
=
x
20
\left(x^{3+y}\right) \cdot x^{5}=x^{20}
(
x
3
+
y
)
⋅
x
5
=
x
20
is true for all values of
x
x
x
. What is the value of
y
y
y
?
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The equation
(
z
3
+
t
)
4
=
z
20
\left(z^{3+t}\right)^{4}=z^{20}
(
z
3
+
t
)
4
=
z
20
is true for all values of
z
z
z
. What is the value of
t
t
t
?
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Evaluate the expression
6
2
+
x
−
x
2
6^{2}+x-x^{2}
6
2
+
x
−
x
2
for
x
=
3
x=3
x
=
3
.
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Evaluate the expression
2
(
5
)
x
2(5)^{x}
2
(
5
)
x
for
x
=
2
x=2
x
=
2
.
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Evaluate the expression
4
x
2
x
\frac{4^{x}}{2^{x}}
2
x
4
x
for
x
=
3
x=3
x
=
3
.
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Evaluate the expression
7
2
x
2
−
2
\frac{7^{2}}{x^{2}-2}
x
2
−
2
7
2
for
x
=
3
x=3
x
=
3
.
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Evaluate the expression
4
x
−
3
x
4^{x}-3^{x}
4
x
−
3
x
for
x
=
2
x=2
x
=
2
.
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Evaluate the expression
10
(
3
)
x
10(3)^{x}
10
(
3
)
x
for
x
=
2
x=2
x
=
2
.
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Evaluate the expression
2
x
−
x
2
2^{x}-x^{2}
2
x
−
x
2
for
x
=
5
x=5
x
=
5
.
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What is the inverse of the function
\newline
g
(
x
)
=
−
2
(
x
−
4
)
?
g(x)=-2(x-4)?
g
(
x
)
=
−
2
(
x
−
4
)?
\newline
g
−
1
(
x
)
=
g^{-1}(x)=
g
−
1
(
x
)
=
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What is the inverse of the function
\newline
f
(
x
)
=
−
6
x
−
7
f(x) = -6x - 7
f
(
x
)
=
−
6
x
−
7
?
\newline
f
−
1
(
x
)
=
f^{-1}(x) =
f
−
1
(
x
)
=
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What is the inverse of the function
\newline
f
(
x
)
=
3
x
−
2
?
f(x)=3x-2 ?
f
(
x
)
=
3
x
−
2
?
\newline
f
−
1
(
x
)
=
f^{-1}(x)=
f
−
1
(
x
)
=
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h
(
1
)
=
h(1)=
h
(
1
)
=
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
e
(
x
+
1
)
f(x) = e^{(x + 1)}
f
(
x
)
=
e
(
x
+
1
)
\newline
f
′
(
x
)
=
f'\left(x\right) =
f
′
(
x
)
=
______
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