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Math Problems
Algebra 2
Simplify variable expressions using properties
Let
g
(
x
)
=
x
−
10
g(x)=x^{-10}
g
(
x
)
=
x
−
10
.
\newline
g
′
(
1
)
=
g^{\prime}(1)=
g
′
(
1
)
=
Get tutor help
d
d
x
(
x
−
8
)
=
\frac{d}{d x}\left(x^{-8}\right)=
d
x
d
(
x
−
8
)
=
Get tutor help
d
d
x
(
x
4
)
=
\frac{d}{d x}(\sqrt[4]{x})=
d
x
d
(
4
x
)
=
Get tutor help
Let
g
(
x
)
=
1
x
3
g(x)=\frac{1}{x^{3}}
g
(
x
)
=
x
3
1
.
\newline
g
′
(
3
)
=
g^{\prime}(3)=
g
′
(
3
)
=
Get tutor help
d
d
x
(
x
2
5
)
=
\frac{d}{d x}\left(\sqrt[5]{x^{2}}\right)=
d
x
d
(
5
x
2
)
=
Get tutor help
Let
f
(
x
)
=
1
x
2
f(x)=\frac{1}{x^{2}}
f
(
x
)
=
x
2
1
.
\newline
f
′
(
5
)
=
f^{\prime}(5)=
f
′
(
5
)
=
Get tutor help
d
d
x
(
x
5
)
=
\frac{d}{d x}\left(\sqrt{x^{5}}\right)=
d
x
d
(
x
5
)
=
Get tutor help
Let
g
(
x
)
=
x
4
3
g(x)=\sqrt[3]{x^{4}}
g
(
x
)
=
3
x
4
.
\newline
g
′
(
x
)
=
g^{\prime}(x)=
g
′
(
x
)
=
Get tutor help
Let
g
(
x
)
=
x
3
4
g(x)=\sqrt[4]{x^{3}}
g
(
x
)
=
4
x
3
.
\newline
g
′
(
1
)
=
g^{\prime}(1)=
g
′
(
1
)
=
Get tutor help
Let
y
=
4
x
2
+
3
x
2
x
−
7
y=\frac{4 x^{2}+3 x}{2 x-7}
y
=
2
x
−
7
4
x
2
+
3
x
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Let
g
(
x
)
=
sin
(
x
)
x
g(x)=\frac{\sin (x)}{\sqrt{x}}
g
(
x
)
=
x
s
i
n
(
x
)
.
\newline
g
′
(
x
)
=
g^{\prime}(x)=
g
′
(
x
)
=
Get tutor help
d
d
x
(
e
x
cos
(
x
)
)
=
\frac{d}{d x}\left(\frac{e^{x}}{\cos (x)}\right)=
d
x
d
(
c
o
s
(
x
)
e
x
)
=
Get tutor help
d
d
x
(
sin
(
x
)
cos
(
x
)
)
=
\frac{d}{d x}\left(\frac{\sin (x)}{\cos (x)}\right)=
d
x
d
(
c
o
s
(
x
)
s
i
n
(
x
)
)
=
Get tutor help
Let
y
=
x
e
x
y=\frac{\sqrt{x}}{e^{x}}
y
=
e
x
x
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
Let
y
=
x
2
+
6
x
10
−
x
2
y=\frac{x^{2}+6 x}{10-x^{2}}
y
=
10
−
x
2
x
2
+
6
x
.
\newline
d
y
d
x
=
\frac{d y}{d x}=
d
x
d
y
=
Get tutor help
d
d
x
(
ln
(
x
)
x
)
=
\frac{d}{d x}\left(\frac{\ln (x)}{\sqrt{x}}\right)=
d
x
d
(
x
l
n
(
x
)
)
=
Get tutor help
Let
f
(
x
)
=
x
2
e
x
f(x)=\frac{x^{2}}{e^{x}}
f
(
x
)
=
e
x
x
2
.
\newline
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
Let
f
(
x
)
=
cos
(
x
)
x
f(x)=\frac{\cos (x)}{x}
f
(
x
)
=
x
c
o
s
(
x
)
.
\newline
f
′
(
x
)
=
f^{\prime}(x)=
f
′
(
x
)
=
Get tutor help
We are given that
d
y
d
x
=
3
x
2
y
\frac{d y}{d x}=3 x^{2} y
d
x
d
y
=
3
x
2
y
.
\newline
Find an expression for
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
in terms of
x
x
x
and
y
y
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
We are given that
d
y
d
x
=
sin
(
y
)
x
\frac{d y}{d x}=\frac{\sin (y)}{x}
d
x
d
y
=
x
s
i
n
(
y
)
.
\newline
Find an expression for
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
in terms of
x
x
x
and
y
y
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
Let
y
=
3
x
y=3^{x}
y
=
3
x
.
\newline
Find
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
Let
y
=
6
ln
(
4
x
)
y=6 \ln (4 x)
y
=
6
ln
(
4
x
)
.
\newline
Find
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
Let
y
=
(
3
x
−
2
)
4
y=(3 x-2)^{4}
y
=
(
3
x
−
2
)
4
.
\newline
Find
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
Let
y
=
3
x
y=3^{x}
y
=
3
x
.
\newline
Find
d
2
y
d
x
2
\frac{d^{2} y}{d x^{2}}
d
x
2
d
2
y
.
\newline
d
2
y
d
x
2
=
\frac{d^{2} y}{d x^{2}}=
d
x
2
d
2
y
=
Get tutor help
Let
f
(
x
)
=
(
2
x
+
1
)
5
f(x)=(2 x+1)^{5}
f
(
x
)
=
(
2
x
+
1
)
5
.
\newline
Find
f
′
′
(
x
)
f^{\prime \prime}(x)
f
′′
(
x
)
.
\newline
f
′
′
(
x
)
=
f^{\prime \prime}(x)=
f
′′
(
x
)
=
Get tutor help
y
=
4
x
+
1
y=\sqrt{4 x+1}
y
=
4
x
+
1
\newline
d
y
d
x
=
?
\frac{d y}{d x}=?
d
x
d
y
=
?
\newline
Choose
1
1
1
answer:
\newline
(A)
2
4
x
+
1
\frac{2}{\sqrt{4 x+1}}
4
x
+
1
2
\newline
(B)
2
4
x
+
1
2 \sqrt{4 x+1}
2
4
x
+
1
\newline
(C)
2
x
\frac{2}{\sqrt{x}}
x
2
\newline
(D)
1
2
4
x
+
1
\frac{1}{2 \sqrt{4 x+1}}
2
4
x
+
1
1
Get tutor help
Reduce to simplest form.
\newline
8
3
+
(
−
9
4
)
=
\frac{8}{3}+\left(-\frac{9}{4}\right)=
3
8
+
(
−
4
9
)
=
Get tutor help
Reduce to simplest form.
\newline
−
1
2
−
3
5
=
-\frac{1}{2}-\frac{3}{5}=
−
2
1
−
5
3
=
Get tutor help
Reduce to simplest form.
\newline
−
1
2
−
2
5
=
-\frac{1}{2}-\frac{2}{5}=
−
2
1
−
5
2
=
Get tutor help
Reduce to simplest form.
\newline
−
5
12
−
(
−
9
3
)
=
-\frac{5}{12}-\left(-\frac{9}{3}\right)=
−
12
5
−
(
−
3
9
)
=
Get tutor help
Reduce to simplest form.
\newline
−
3
2
−
3
8
=
-\frac{3}{2}-\frac{3}{8}=
−
2
3
−
8
3
=
Get tutor help
Reduce to simplest form.
\newline
−
5
8
−
(
−
4
3
)
=
-\frac{5}{8}-\left(-\frac{4}{3}\right)=
−
8
5
−
(
−
3
4
)
=
Get tutor help
Reduce to simplest form.
\newline
−
7
12
+
3
8
=
-\frac{7}{12}+\frac{3}{8}=
−
12
7
+
8
3
=
Get tutor help
Combine the like terms to create an equivalent expression:
\newline
2
s
+
(
−
4
s
)
=
0
2s+(-4s)=\boxed{\phantom{0}}
2
s
+
(
−
4
s
)
=
0
Get tutor help
Combine the like terms to create an equivalent expression:
\newline
−
4
p
+
(
−
6
p
)
=
□
-4p+(-6p)=\square
−
4
p
+
(
−
6
p
)
=
□
Get tutor help
Combine the like terms to create an equivalent expression:
\newline
4
z
−
(
−
3
z
)
=
□
4z-(-3z)=\square
4
z
−
(
−
3
z
)
=
□
Get tutor help
Combine the like terms to create an equivalent expression:
\newline
r
+
(
−
5
r
)
=
0
r+(-5r)=\boxed{\phantom{0}}
r
+
(
−
5
r
)
=
0
Get tutor help
Combine the like terms to create an equivalent expression:
\newline
−
4
p
+
(
−
2
)
+
2
p
+
3
=
-4p+(-2)+2p+3=
−
4
p
+
(
−
2
)
+
2
p
+
3
=
Get tutor help
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