Esercizio
$\frac{d}{dx}\left(\sqrt{xy}=2x-y\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx((xy)^(1/2)=2x-y). Applicare la formula: \left(ab\right)^n=a^nb^n. Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=\sqrt{x}\sqrt{y} e b=2x-y. 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=\sqrt{x}\sqrt{y}, a=\sqrt{x}, b=\sqrt{y} e d/dx?ab=\frac{d}{dx}\left(\sqrt{x}\sqrt{y}\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=\frac{1}{2} e x=y.
Risposta finale al problema
$y^{\prime}=2+\frac{-\sqrt{y}}{2\sqrt{x}}+\frac{-\sqrt{x}y^{\left({\prime}-\frac{1}{2}\right)}}{2}$