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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 or more functions is the sum of the derivatives of each function

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

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

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

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

$2\cdot 1y$

Any expression multiplied by $1$ is equal to itself

$2y$
6

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 $-1$

$2x$
7

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

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

Final Answer

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

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