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