Simplify the expression $\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^2}}{3x}\right)$

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Final answer to the problem

$\frac{2+24\sqrt[3]{x^{5}}-\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{3}\right)}-12\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}+\frac{4}{3}\right)}}{3x^{\left(\frac{1}{3}+\frac{1}{2}\right)}}$
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Step-by-step Solution

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  • Simplify
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Find the integral
  • Find the derivative
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1

Simplify $\sqrt[3]{x^2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $\frac{1}{3}$

$\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^{2}}}{3x}\right)$

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$\left(\frac{2}{\sqrt{x}}-\sqrt{3}\right)\left(4x\sqrt[3]{x}+\frac{\sqrt[3]{x^{2}}}{3x}\right)$

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Unlock the first 3 steps of this solution

Learn how to solve equations problems step by step online. Simplify the expression (2/(x^(1/2))-3^(1/2))(4xx^(1/3)+(x^2^(1/3))/(3x)). Simplify \sqrt[3]{x^2} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals \frac{1}{3}. When multiplying exponents with same base you can add the exponents: 4x\sqrt[3]{x}. Simplify the fraction \frac{\sqrt[3]{x^{2}}}{3x} by x. Combine \frac{2}{\sqrt{x}}-\sqrt{3} in a single fraction.

Final answer to the problem

$\frac{2+24\sqrt[3]{x^{5}}-\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{3}\right)}-12\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}+\frac{4}{3}\right)}}{3x^{\left(\frac{1}{3}+\frac{1}{2}\right)}}$

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Function Plot

Plotting: $\frac{2+24\sqrt[3]{x^{5}}-\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}-\frac{1}{3}\right)}-12\sqrt{3}x^{\left(\frac{1}{2}+\frac{1}{3}+\frac{4}{3}\right)}}{3x^{\left(\frac{1}{3}+\frac{1}{2}\right)}}$

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5
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7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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