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Calcolatrice di Differenziazione implicita

Risolvete i vostri problemi di matematica con la nostra calcolatrice Differenziazione implicita passo-passo. Migliorate le vostre abilità matematiche con il nostro ampio elenco di problemi impegnativi. Trova tutte le nostre calcolatrici qui.

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 Esempio

 Problemi risolti

 Problemi difficili

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 $y$

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

 Risposta finale al problema

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

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