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