Esercizio
$\frac{d}{dx}\left(30x^{\frac{1}{3}}y^{\frac{2}{3}}\:=\:360\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(30x^(1/3)y^(2/3)=360). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=30\sqrt[3]{x}\sqrt[3]{y^{2}} e b=360. Applicare la formula: \frac{d}{dx}\left(c\right)=0, dove c=360. 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=\sqrt[3]{x}\sqrt[3]{y^{2}}, a=\sqrt[3]{x}, b=\sqrt[3]{y^{2}} e d/dx?ab=\frac{d}{dx}\left(\sqrt[3]{x}\sqrt[3]{y^{2}}\right).
d/dx(30x^(1/3)y^(2/3)=360)
Risposta finale al problema
$y^{\prime}=\frac{-y}{2x}$