Risolvere: $\frac{d}{dx}\left(\sqrt{xy}=x^6y\right)$
Esercizio
$\frac{dy}{dx}\left(\sqrt{xy}=x^6y\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di limiti all'infinito passo dopo passo. d/dx((xy)^(1/2)=x^6y). 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=x^6y. 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(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=x^6y, a=x^6, b=y e d/dx?ab=\frac{d}{dx}\left(x^6y\right).
Risposta finale al problema
$y^{\prime}=\frac{12\sqrt{y^{3}}\sqrt{x^{11}}-y}{\sqrt{x}\left(\sqrt{x}-2x^{6}\sqrt{y}\right)}$