Risolvere: $\frac{d}{dx}\left(\left(5xy\right)^{0.5}=8+x^2y\right)$
Esercizio
$\frac{dy}{dx}\left(sqrt\left(5xy\right)=8+x^2y\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx((5xy)^1/2=8+x^2y). 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=5^{0.5}x^{0.5}y^{0.5} e b=8+x^2y. 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=x^{0.5}y^{0.5}, a=x^{0.5}, b=y^{0.5} e d/dx?ab=\frac{d}{dx}\left(x^{0.5}y^{0.5}\right).
Risposta finale al problema
$y^{\prime}=\frac{-2yx^{1.5}+0.55^{0.5}y^{0.5}+0.55^{0.5}xy^{\left({\prime}-0.5\right)}}{x^{2.5}}$