Try NerdPal! Our new app on iOS and Android

# Find the implicit derivative $\frac{d}{dx}\left(2xy=1\right)$

## Step-by-step Solution

Go!
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

### Videos

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

## Step-by-step Solution

Problem to solve:

$\frac{d}{dx}\left(2xy=1\right)$

Specify the solving method

1

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

$\frac{d}{dx}\left(2xy\right)=\frac{d}{dx}\left(1\right)$

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

$\frac{d}{dx}\left(2xy\right)=\frac{d}{dx}\left(1\right)$

Learn how to solve implicit differentiation problems step by step online. Find the implicit derivative (d/dx)(2xy=1). Apply implicit differentiation by taking the derivative of both sides of the equation with respect to the differentiation variable. The derivative of the constant function (1) is equal to zero. The derivative of a function multiplied by a constant (2) 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.

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

$\frac{d}{dx}\left(2xy=1\right)$

### Main topic:

Implicit Differentiation

~ 0.07 s