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Math Problems
Calculus
Find derivatives using the product rule I
if
f
(
x
)
=
1.
5
x
+
1
f(x) = 1.5^x + 1
f
(
x
)
=
1.
5
x
+
1
, what is the value of
f
(
2
)
f(2)
f
(
2
)
?
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If
1
1
a
=
1
1
5
6
11^a=\sqrt[6]{11^5}
1
1
a
=
6
1
1
5
, what is the value of
a
a
a
?
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1
6
x
2
+
y
+
1
6
x
+
y
2
16^{x^2}+y+16^x+y^2
1
6
x
2
+
y
+
1
6
x
+
y
2
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Solve the following equation:
\newline
3
x
+
5
y
=
52
3^x+5^y=52
3
x
+
5
y
=
52
\newline
3
x
−
5
y
=
2
3^x-5^y=2
3
x
−
5
y
=
2
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Select all the expressions that are equivalent to
6
4
3
4
\frac{6^4}{3^4}
3
4
6
4
.
\newline
Multi-select Choices:
\newline
(A)
1
2
−
4
\frac{1}{2^{-4}}
2
−
4
1
\newline
(B)
2
0
2^0
2
0
\newline
(C)
2
2
2
\newline
(D)
1
2
4
\frac{1}{2^4}
2
4
1
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In the following equation, what is the value of
z
z
z
?
\newline
6
2
=
6
z
6
3
6^2 = \frac{6^z}{6^3}
6
2
=
6
3
6
z
\newline
z
=
z =
z
=
____
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Select all the expressions that are equivalent to
6
4
3
4
\frac{6^4}{3^4}
3
4
6
4
.
\newline
Multi-select Choices:
\newline
(A)
1
2
4
\frac{1}{2^4}
2
4
1
\newline
(B)
2
2
2
\newline
(C)
2
4
2^4
2
4
\newline
(D)
1
2
−
4
\frac{1}{2^{-4}}
2
−
4
1
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Solve the equation for
𝑥
𝑥
x
:
2
x
+
17
=
3
x
−
2
2^x + 17 = 3^x - 2
2
x
+
17
=
3
x
−
2
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How does
f
(
t
)
=
2
t
f(t) = 2^t
f
(
t
)
=
2
t
change over the interval from
t
=
1
t = 1
t
=
1
to
t
=
2
t = 2
t
=
2
?
\newline
Choices:
\newline
(A)
f
(
t
)
f(t)
f
(
t
)
decreases by
2
%
2\%
2%
\newline
(B)
f
(
t
)
f(t)
f
(
t
)
increases by
200
%
200\%
200%
\newline
(C)
f
(
t
)
f(t)
f
(
t
)
increases by a factor of
2
2
2
\newline
(D)
f
(
t
)
f(t)
f
(
t
)
increases by
2
2
2
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Show that there exist irrational numbers
x
,
y
x,y
x
,
y
for which
x
y
x^y
x
y
is rational
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4
2
+
4
2
+
4
2
+
4
2
=
2
n
4^2+4^2+4^2+4^2=2^n
4
2
+
4
2
+
4
2
+
4
2
=
2
n
what is the value of
n
n
n
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Solve for
x
x
x
:
x
2
+
3
x
−
10
=
0
x^{2} + 3x - 10 = 0
x
2
+
3
x
−
10
=
0
a
=
1
a=1
a
=
1
,
b
=
3
b=3
b
=
3
, and
c
=
−
10
c=-10
c
=
−
10
.
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Find the derivative of
f
(
x
)
f(x)
f
(
x
)
.
\newline
f
(
x
)
=
x
e
x
f(x) = x e^x
f
(
x
)
=
x
e
x
\newline
f
′
(
x
)
=
f'\left(x\right) =
f
′
(
x
)
=
______
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