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