👉 Try now NerdPal! Our new math app on iOS and Android
  1. calculators
  2. Implicit Differentiation

Implicit Differentiation Calculator

Get detailed solutions to your math problems with our Implicit Differentiation step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

Go!
Symbolic mode
Text mode
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

1

Here, we show you a step-by-step solved example of implicit differentiation. This solution was automatically generated by our smart calculator:

$\frac{d}{dx}\left(x^2+y^2=16\right)$
2

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

$\frac{d}{dx}\left(x^2+y^2\right)=\frac{d}{dx}\left(16\right)$
3

The derivative of the constant function ($16$) is equal to zero

$\frac{d}{dx}\left(x^2+y^2\right)=0$
4

The derivative of a sum of two or more functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(y^2\right)=0$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{d}{dx}\left(x^2\right)+2y^{2-1}\frac{d}{dx}\left(y\right)=0$

Add the values $2$ and $-1$

$\frac{d}{dx}\left(x^2\right)+2y^{1}\frac{d}{dx}\left(y\right)=0$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2y^{2-1}\frac{d}{dx}\left(y\right)$

Subtract the values $2$ and $-1$

$2y^{1}\frac{d}{dx}\left(y\right)$
5

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$\frac{d}{dx}\left(x^2\right)+2y^{1}\frac{d}{dx}\left(y\right)=0$
6

Any expression to the power of $1$ is equal to that same expression

$\frac{d}{dx}\left(x^2\right)+2y\frac{d}{dx}\left(y\right)=0$
7

The derivative of the linear function is equal to $1$

$\frac{d}{dx}\left(x^2\right)+2y\cdot y^{\prime}=0$

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2x^{\left(2-1\right)}$

Subtract the values $2$ and $-1$

$2x$
8

The power rule for differentiation states that if $n$ is a real number and $f(x) = x^n$, then $f'(x) = nx^{n-1}$

$2x+2y\cdot y^{\prime}=0$
9

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $2x$ from both sides of the equation

$2y\cdot y^{\prime}=-2x$
10

Divide both sides of the equation by $2$

$y^{\prime}y=\frac{-2x}{2}$
11

Take $\frac{-2}{2}$ out of the fraction

$y^{\prime}y=-x$
12

Divide both sides of the equation by $y$

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

Final answer to the problem

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

Are you struggling with math?

Access detailed step by step solutions to thousands of problems, growing every day!