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Math Problems
Calculus
Find derivatives using the chain rule II
Differentiate:
y
=
(
x
−
1
)
2
y=(x-1)^{2}
y
=
(
x
−
1
)
2
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y
=
−
(
x
+
7
)
2
−
9
y=-(x+7)^2-9
y
=
−
(
x
+
7
)
2
−
9
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Find the inverse of each function.
\newline
f
(
x
)
=
−
2
−
3
x
2
f(x)=\frac{-2-3 x}{2}
f
(
x
)
=
2
−
2
−
3
x
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∑
n
=
0
2
(
n
)
=
\sum_{n=0}^{2}(n)=
∑
n
=
0
2
(
n
)
=
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∑
x
=
1
3
(
4
x
)
=
\sum_{x=1}^{3}(4 x)=
∑
x
=
1
3
(
4
x
)
=
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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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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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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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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
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
−
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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