Esercizio
$\frac{d}{dx}y^3=\sqrt[3]{5x^3+3x^{\frac{2}{3}}y^{\frac{2}{3}}}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(y^3=(5x^3+3x^(2/3)y^(2/3))^(1/3)). Applicare la formula: \frac{d}{dx}\left(a=b\right)=\frac{d}{dx}\left(a\right)=\frac{d}{dx}\left(b\right), dove a=y^3 e b=\sqrt[3]{5x^3+3\sqrt[3]{x^{2}}\sqrt[3]{y^{2}}}. Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=3 e x=y. 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}{3} e x=5x^3+3\sqrt[3]{x^{2}}\sqrt[3]{y^{2}}. Applicare la formula: \frac{d}{dx}\left(x\right)=1.
d/dx(y^3=(5x^3+3x^(2/3)y^(2/3))^(1/3))
Risposta finale al problema
$3y^{2}y^{\prime}=\frac{1}{3\sqrt[3]{\left(5x^3+3\sqrt[3]{x^{2}}\sqrt[3]{y^{2}}\right)^{2}}}\left(15x^{2}+\frac{2\sqrt[3]{y^{2}}}{\sqrt[3]{x}}+\sqrt[3]{x^{2}}\frac{2}{\sqrt[3]{y}}y^{\prime}\right)$