Esercizio
$\frac{d}{dx}\sqrt{\frac{x-3}{x^6+4}}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(((x-3)/(x^6+4))^(1/2)). 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-3}{x^6+4}. Applicare la formula: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, dove a=x-3, b=x^6+4 e n=-\frac{1}{2}. Applicare la formula: \frac{d}{dx}\left(\frac{a}{b}\right)=\frac{\frac{d}{dx}\left(a\right)b-a\frac{d}{dx}\left(b\right)}{b^2}, dove a=x-3 e b=x^6+4. Applicare la formula: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, dove a=1, b=2, c=\frac{d}{dx}\left(x-3\right)\left(x^6+4\right)-\left(x-3\right)\frac{d}{dx}\left(x^6+4\right), a/b=\frac{1}{2}, f=\left(x^6+4\right)^2, c/f=\frac{\frac{d}{dx}\left(x-3\right)\left(x^6+4\right)-\left(x-3\right)\frac{d}{dx}\left(x^6+4\right)}{\left(x^6+4\right)^2} e a/bc/f=\frac{1}{2}\sqrt{\frac{x^6+4}{x-3}}\frac{\frac{d}{dx}\left(x-3\right)\left(x^6+4\right)-\left(x-3\right)\frac{d}{dx}\left(x^6+4\right)}{\left(x^6+4\right)^2}.
d/dx(((x-3)/(x^6+4))^(1/2))
Risposta finale al problema
$\frac{x^6+4+6\left(-x+3\right)x^{5}}{2\left(x^6+4\right)^2}\sqrt{\frac{x^6+4}{x-3}}$