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Topics
Pre-Algebra
Mean
Mode
Greatest Common Factor
Least Common Multiple
Order of Operations
Fractions
Mixed Fractions
Prime Factorization
Exponents
Radicals
Algebra
Combine Like Terms
Solve for a Variable
Factor
Expand
Evaluate Fractions
Linear Equations
Quadratic Equations
Inequalities
Systems of Equations
Matrices
Trigonometry
Simplify
Evaluate
Graphs
Solve Equations
Calculus
Derivatives
Integrals
Limits
Algebra Calculator
Trigonometry Calculator
Calculus Calculator
Matrix Calculator
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Evaluate
3x^{4}
3
x
4
View solution steps
Solution Steps
x \cdot x^2 \cdot 3x
x
⋅
x
2
⋅
3
x
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
To multiply powers of the same base, add their exponents. Add
1
and
2
to get
3
.
x^{3}\times 3x
x
3
×
3
x
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
To multiply powers of the same base, add their exponents. Add
3
and
1
to get
4
.
x^{4}\times 3
x
4
×
3
Differentiate w.r.t. x
12x^{3}
1
2
x
3
View solution steps
Steps Using Definition of a Derivative
x \cdot x^2 \cdot 3x
x
⋅
x
2
⋅
3
x
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
To multiply powers of the same base, add their exponents. Add
1
and
2
to get
3
.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 3x)
d
x
d
(
x
3
×
3
x
)
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
To multiply powers of the same base, add their exponents. Add
3
and
1
to get
4
.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 3)
d
x
d
(
x
4
×
3
)
The derivative of ax^{n} is nax^{n-1}.
The derivative of
a
x
n
is
n
a
x
n
−
1
.
4\times 3x^{4-1}
4
×
3
x
4
−
1
Multiply 4 times 3.
Multiply
4
times
3
.
12x^{4-1}
1
2
x
4
−
1
Subtract 1 from 4.
Subtract
1
from
4
.
12x^{3}
1
2
x
3
Graph
Quiz
Polynomial
5 problems similar to:
x \cdot x^2 \cdot 3x
x
⋅
x
2
⋅
3
x
Similar Problems from Web Search
How do you solve \displaystyle{2}\cdot{3}^{{{10}{x}+{6}}}={18} ?
How do you solve
2
⋅
3
1
0
x
+
6
=
1
8
?
https://socratic.org/questions/how-do-you-solve-2-cdot-3-10x-6-18
The solution is \displaystyle=-\frac{{2}}{{5}} Explanation: The equation is \displaystyle{2}\cdot{3}^{{{10}{x}+{6}}}={18} Dividing by \displaystyle{2} \displaystyle{3}^{{{10}{x}+{6}}}=\frac{{18}}{{2}}={9}={3}^{{2}} ...
The solution is
=
−
5
2
Explanation: The equation is
2
⋅
3
1
0
x
+
6
=
1
8
Dividing by
2
3
1
0
x
+
6
=
2
1
8
=
9
=
3
2
...
How do you multiply \displaystyle{x}^{{{2}}}\cdot{x}^{{{8}}}\cdot{x} ?
How do you multiply
x
2
⋅
x
8
⋅
x
?
https://socratic.org/questions/how-do-you-multiply-x-2-cdot-x-8-cdot-x
Add the exponents \displaystyle{x}^{{{2}+{8}+{1}}} = \displaystyle{x}^{{11}} Explanation: \displaystyle{x}^{{2}}={x}\times{x} \displaystyle{x}^{{8}}={x}\times{x}\times{x}\times{x}\times{x}\times{x}\times{x}\times{x} ...
Add the exponents
x
2
+
8
+
1
=
x
1
1
Explanation:
x
2
=
x
×
x
x
8
=
x
×
x
×
x
×
x
×
x
×
x
×
x
×
x
...
How do you solve \displaystyle{2}^{{{x}}}\cdot{3}^{{{2}{x}-{1}}}={5}^{{{x}+{1}}} ?
How do you solve
2
x
⋅
3
2
x
−
1
=
5
x
+
1
?
https://socratic.org/questions/how-do-you-solve-2-x-cdot-3-2x-1-5-x-1
\displaystyle{x}=={2.1141} Explanation: Taking logarithm (base10) on both sides of \displaystyle{2}^{{x}}\cdot{3}^{{{2}{x}-{1}}}={5}^{{{x}+{1}}} , we get \displaystyle{x}{\log{{2}}}+{\left({2}{x}-{1}\right)}{\log{{3}}}={\left({x}+{1}\right)}{\log{{5}}} ...
x
=
=
2
.
1
1
4
1
Explanation: Taking logarithm (base10) on both sides of
2
x
⋅
3
2
x
−
1
=
5
x
+
1
, we get
x
lo
g
2
+
(
2
x
−
1
)
lo
g
3
=
(
x
+
1
)
lo
g
5
...
How do you graph \displaystyle{f{{\left({x}\right)}}}={2}\cdot{3}^{{x}} ?
How do you graph
f
(
x
)
=
2
⋅
3
x
?
https://socratic.org/questions/how-do-you-graph-f-x-2-3-x
See below Explanation: Let's first notice that the graph of \displaystyle{3}^{{x}} will have a \displaystyle{y}- intercept of 1 (anything taken to the power of 0 is 1). Then at \displaystyle{x}={1},{y}={3} ...
See below Explanation: Let's first notice that the graph of
3
x
will have a
y
−
intercept of 1 (anything taken to the power of 0 is 1). Then at
x
=
1
,
y
=
3
...
A few questions about derivative notation
A few questions about derivative notation
https://math.stackexchange.com/questions/1203598/a-few-questions-about-derivative-notation
1) How do I denote derivative of ax^2 +b in terms of ax^2 ? (ax^2 +b) ′ (ax^2 ) can easily be confused with ax^2 \cdot (ax^2 +b) ′ . Ah. Where as the prime notation on a function symbol ...
1) How do I denote derivative of
a
x
2
+
b
in terms of
a
x
2
?
(
a
x
2
+
b
)
′
(
a
x
2
)
can easily be confused with
a
x
2
⋅
(
a
x
2
+
b
)
′
. Ah. Where as the prime notation on a function symbol ...
If g:\mathbb{N}\rightarrow \mathbb{R} and g(m+n)+g(m-n)=2g(m)+2g(n) what is g(x)
If
g
:
N
→
R
and
g
(
m
+
n
)
+
g
(
m
−
n
)
=
2
g
(
m
)
+
2
g
(
n
)
what is
g
(
x
)
https://math.stackexchange.com/questions/1768488/if-g-mathbbn-rightarrow-mathbbr-and-gmngm-n-2gm2gn-what-is
We have that g(0)=0 because, with m=1,n=0, g(1)+g(1)=2g(1)+2g(0). Now g(n+1)+g(n-1)=2g(n)+2g(1), thus g(n+1)=2g(n)-g(n-1)+2. By induction, we suppose that g(k)=k^2 for k\leq n. This is ...
We have that
g
(
0
)
=
0
because, with
m
=
1
,
n
=
0
,
g
(
1
)
+
g
(
1
)
=
2
g
(
1
)
+
2
g
(
0
)
. Now
g
(
n
+
1
)
+
g
(
n
−
1
)
=
2
g
(
n
)
+
2
g
(
1
)
, thus
g
(
n
+
1
)
=
2
g
(
n
)
−
g
(
n
−
1
)
+
2
. By induction, we suppose that
g
(
k
)
=
k
2
for
k
≤
n
. This is ...
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x^{3}\times 3x
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
x^{4}\times 3
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 3x)
To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 3)
To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.
4\times 3x^{4-1}
The derivative of ax^{n} is nax^{n-1}.
12x^{4-1}
Multiply 4 times 3.
12x^{3}
Subtract 1 from 4.
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x \cdot x^2 \cdot 3x
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⋅
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⋅
3
x
n^4 \cdot 2n^2 \cdot n^5
n
4
⋅
2
n
2
⋅
n
5
(2a \cdot 3b^2)^2 \cdot c \cdot (2bc^3)^3
(
2
a
⋅
3
b
2
)
2
⋅
c
⋅
(
2
b
c
3
)
3
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b
a
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2
\frac{x^3y^5}{3x} \times \frac{y^4}{x^2}
3
x
x
3
y
5
×
x
2
y
4
\frac{x^3y^5}{3x} \div \frac{y^4}{x^2}
3
x
x
3
y
5
÷
x
2
y
4
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