Esercizio
$\frac{d^3}{dx^3}\left(x^2+y^2=1\right)$
Soluzione passo-passo
Passi intermedi
1
Trovare la derivata ($1$)
$2x+2y\frac{d}{dx}\left(y\right)=0$
Passi intermedi
2
Trovare la derivata ($2$)
$2+2\frac{d^2}{dx^2}\left(y\right)y+2\left(\frac{d}{dx}\left(y\right)\right)^2=0$
Passi intermedi
3
Trovare la derivata ($3$)
$2\frac{d}{dx}\left(\frac{d^2}{dx^2}\left(y\right)\right)y+4\frac{d}{dx}\left(y\right)\frac{d^2}{dx^2}\left(y\right)+2\frac{d^2}{dx^2}\left(y\right)\frac{d}{dx}\left(y\right)=0$
Passi intermedi
$2\frac{d}{dx}\left(\frac{d^2}{dx^2}\left(y\right)\right)y+6\frac{d^2}{dx^2}\left(y\right)\frac{d}{dx}\left(y\right)=0$
Risposta finale al problema
$2\frac{d}{dx}\left(\frac{d^2}{dx^2}\left(y\right)\right)y+6\frac{d^2}{dx^2}\left(y\right)\frac{d}{dx}\left(y\right)=0$