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Find the implicit derivative $\frac{d}{dx}\left(x^3+y^3=6xy\right)$

Step-by-step Solution

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Final answer to the problem

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

How should I solve this problem?

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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

$\frac{d}{dx}\left(x^3+y^3\right)=\frac{d}{dx}\left(6xy\right)$

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$\frac{d}{dx}\left(x^3+y^3\right)=\frac{d}{dx}\left(6xy\right)$

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Learn how to solve problems step by step online. Find the implicit derivative d/dx(x^3+y^3=6xy). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of a function multiplied by a constant is equal to the constant times the derivative of the function. Apply the product rule for differentiation: (f\cdot g)'=f'\cdot g+f\cdot g', where f=. The derivative of the linear function is equal to 1.

Final answer to the problem

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

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

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

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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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