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Implicit differentiation Calculator

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1

Solved example of implicit differentiation

$\frac{d}{dx}\left(x^2+y^2=16\right)$
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 functions is the sum of the derivatives of each function

$\frac{d}{dx}\left(x^2\right)+\frac{d}{dx}\left(y^2\right)=0$
5

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

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

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

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

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

$2x+2yy^{\prime}=0$
8

Subtract $2x$ from both sides of the equation

$2yy^{\prime}=-2x$
9

Divide both sides of the equation by $2$

$yy^{\prime}=\frac{-2x}{2}$
10

Divide both sides of the equation by $y$

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

Answer

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

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