Esercizio
$\frac{d^2}{dx^2}\left(\sqrt{x+y}+xy=21\right)$
Soluzione passo-passo
Passi intermedi
1
Trovare la derivata ($1$)
$\frac{1}{2}\left(x+y\right)^{-\frac{1}{2}}\left(1+\frac{d}{dx}\left(y\right)\right)+y+x\frac{d}{dx}\left(y\right)=0$
Passi intermedi
2
Trovare la derivata ($2$)
$\frac{1}{2}\left(-\frac{1}{2}\left(x+y\right)^{-\frac{3}{2}}\left(1+\frac{d}{dx}\left(y\right)\right)^2+\left(x+y\right)^{-\frac{1}{2}}\frac{d^2}{dx^2}\left(y\right)\right)+2\frac{d}{dx}\left(y\right)+x\frac{d^2}{dx^2}\left(y\right)=0$
Risposta finale al problema
$\frac{1}{2}\left(-\frac{1}{2}\left(x+y\right)^{-\frac{3}{2}}\left(1+\frac{d}{dx}\left(y\right)\right)^2+\left(x+y\right)^{-\frac{1}{2}}\frac{d^2}{dx^2}\left(y\right)\right)+2\frac{d}{dx}\left(y\right)+x\frac{d^2}{dx^2}\left(y\right)=0$