Risolvere: $\frac{d}{dx}\left(x\sqrt{\frac{x^2-9}{x^2+9}}\right)$
Esercizio
$\frac{dy}{dx}\left(x\sqrt{\frac{x^2-9}{x^2+9}}\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x((x^2-9)/(x^2+9))^(1/2)). 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\sqrt{\frac{x^2-9}{x^2+9}}, a=x, b=\sqrt{\frac{x^2-9}{x^2+9}} e d/dx?ab=\frac{d}{dx}\left(x\sqrt{\frac{x^2-9}{x^2+9}}\right). Applicare la formula: \frac{d}{dx}\left(x\right)=1. 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=\frac{x^2-9}{x^2+9}. Applicare la formula: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, dove a=x^2-9, b=x^2+9 e n=-\frac{1}{2}.
d/dx(x((x^2-9)/(x^2+9))^(1/2))
Risposta finale al problema
$\sqrt{\frac{x^2-9}{x^2+9}}+\frac{\left(2x\left(x^2+9\right)+2\left(-x^2+9\right)x\right)x\sqrt{\frac{x^2+9}{x^2-9}}}{2\left(x^2+9\right)^2}$