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Simplify the expression $\sqrt{xy}\sqrt[4]{2x^2y}\sqrt[5]{3x^3y^2}$

Step-by-step Solution

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Final answer to the problem

$2.3702914\sqrt[5]{x^{3}}\sqrt[20]{y^{23}}+1.4814321\left(\frac{1}{2\sqrt{x}\sqrt{y}}\right)\sqrt[10]{x^{21}}\sqrt[20]{y^{13}}y^{\prime}+0.9629309\sqrt[5]{x^{8}}\sqrt[20]{y^{3}}$
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Step-by-step Solution

How should I solve this problem?

  • Solve by implicit differentiation
  • Solve by quadratic formula (general formula)
  • Find the derivative using the definition
  • Simplify
  • Find the integral
  • Find the derivative
  • Factor
  • Factor by completing the square
  • Find the roots
  • Find break even points
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1

Apply the product rule for differentiation: $(f\cdot g)'=f'\cdot g+f\cdot g'$

$\frac{d}{dx}\left(\sqrt{xy}\right)\sqrt[4]{2x^2y}\sqrt[5]{3x^3y^2}+\sqrt{xy}\left(\frac{d}{dx}\left(\sqrt[4]{2x^2y}\right)\sqrt[5]{3x^3y^2}+\sqrt[4]{2x^2y}\frac{d}{dx}\left(\sqrt[5]{3x^3y^2}\right)\right)$

Learn how to solve equations problems step by step online.

$\frac{d}{dx}\left(\sqrt{xy}\right)\sqrt[4]{2x^2y}\sqrt[5]{3x^3y^2}+\sqrt{xy}\left(\frac{d}{dx}\left(\sqrt[4]{2x^2y}\right)\sqrt[5]{3x^3y^2}+\sqrt[4]{2x^2y}\frac{d}{dx}\left(\sqrt[5]{3x^3y^2}\right)\right)$

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Learn how to solve equations problems step by step online. Simplify the expression (xy)^1/2(2x^2y)^1/4(3x^3y^2)^1/5. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g'. The power of a product is equal to the product of it's factors raised to the same power. The power of a product is equal to the product of it's factors raised to the same power. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function.

Final answer to the problem

$2.3702914\sqrt[5]{x^{3}}\sqrt[20]{y^{23}}+1.4814321\left(\frac{1}{2\sqrt{x}\sqrt{y}}\right)\sqrt[10]{x^{21}}\sqrt[20]{y^{13}}y^{\prime}+0.9629309\sqrt[5]{x^{8}}\sqrt[20]{y^{3}}$

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Function Plot

Plotting: $2.3702914\sqrt[5]{x^{3}}\sqrt[20]{y^{23}}+1.4814321\left(\frac{1}{2\sqrt{x}\sqrt{y}}\right)\sqrt[10]{x^{21}}\sqrt[20]{y^{13}}y^{\prime}+0.9629309\sqrt[5]{x^{8}}\sqrt[20]{y^{3}}$

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0
a
b
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d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
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

How to improve your answer:

Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.

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