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Find the implicit derivative $\frac{d}{dx}\left(\left(x^2+y^2\right)^2+xy=4x\right)$

Step-by-step Solution

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Final Answer

$y^{\prime}=\frac{4-y-4x^{3}-4xy^2}{4x^2y+4y^{3}+x}$
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Step-by-step Solution

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Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable

$\frac{d}{dx}\left(\left(x^2+y^2\right)^2+xy\right)=\frac{d}{dx}\left(4x\right)$

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$\frac{d}{dx}\left(\left(x^2+y^2\right)^2+xy\right)=\frac{d}{dx}\left(4x\right)$

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Learn how to solve differential calculus problems step by step online. Find the implicit derivative d/dx((x^2+y^2)^2+xy=4x). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the linear function times a constant, is equal to the constant. The derivative of the linear function is equal to 1. The derivative of a sum of two or more functions is the sum of the derivatives of each function.

Final Answer

$y^{\prime}=\frac{4-y-4x^{3}-4xy^2}{4x^2y+4y^{3}+x}$

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Function Plot

Plotting: $y^{\prime}=\frac{4-y-4x^{3}-4xy^2}{4x^2y+4y^{3}+x}$

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5
6
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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Main Topic: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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