Risolvere: $\frac{d}{dx}\left(2xy=-2xe^{-x^2}\right)$
Esercizio
$\frac{dy}{dx}\left(+2xy=-2xe^{-x^2}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(2xy=-2xe^(-x^2)). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=2xy e b=-2xe^{-x^2}. Applicare la formula: \frac{d}{dx}\left(cx\right)=c\frac{d}{dx}\left(x\right). Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=xy, a=x, b=y e d/dx?ab=\frac{d}{dx}\left(xy\right). Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=xe^{-x^2}, a=x, b=e^{-x^2} e d/dx?ab=\frac{d}{dx}\left(xe^{-x^2}\right).
Risposta finale al problema
$y^{\prime}=\frac{-e^{-x^2}+2x^2e^{-x^2}-y}{x}$