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

## Step-by-step Solution

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ln
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asin
acos
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sinh
cosh
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asinh
acosh
atanh
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### Videos

$y^{\prime}=\frac{y-x^{2}}{y^2-x}$
Got another answer? Verify it here!

## Step-by-step Solution

Problem to solve:

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

Specify the solving method

1

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

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

Learn how to solve implicit differentiation problems step by step online.

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

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(x^3+y^3=3xy). 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 (3) 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=x and g=y. The derivative of the linear function is equal to 1.

$y^{\prime}=\frac{y-x^{2}}{y^2-x}$
SnapXam A2

### beta Got another answer? Verify it!

Go!
1
2
3
4
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

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