Find the implicit derivative $\frac{d}{dx}\left(\left(x-y\right)^3=\left(x+y\right)^2\right)$

Step-by-step Solution

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Final answer to the problem

$3\left(x-y\right)^{2}\left(1-y^{\prime}\right)=2\left(x+y\right)\left(1+y^{\prime}\right)$
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Step-by-step Solution

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  • Find the derivative using the definition
  • Find the derivative using the product rule
  • Find the derivative using the quotient rule
  • Find the derivative using logarithmic differentiation
  • Find the derivative
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

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

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$\frac{d}{dx}\left(\left(x-y\right)^3\right)=\frac{d}{dx}\left(\left(x+y\right)^2\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx((x-y)^3=(x+y)^2). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. The power rule for differentiation states that if n is a real number and f(x) = x^n, then f'(x) = nx^{n-1}. Any expression to the power of 1 is equal to that same expression.

Final answer to the problem

$3\left(x-y\right)^{2}\left(1-y^{\prime}\right)=2\left(x+y\right)\left(1+y^{\prime}\right)$

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Function Plot

Plotting: $3\left(x-y\right)^{2}\left(1-y^{\prime}\right)=2\left(x+y\right)\left(1+y^{\prime}\right)$

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1
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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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