Esercizio
$\frac{d}{dx}y=\sqrt[7]{\frac{x-6}{x+4}}$
Soluzione passo-passo
Impara online a risolvere i problemi di semplificare le espressioni trigonometriche passo dopo passo. d/dx(((x-6)/(x+4))^(1/7)). 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}{7} e x=\frac{x-6}{x+4}. Applicare la formula: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, dove a=x-6, b=x+4 e n=-\frac{6}{7}. 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-6 e b=x+4. Applicare la formula: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, dove a=1, b=7, c=\frac{d}{dx}\left(x-6\right)\left(x+4\right)-\left(x-6\right)\frac{d}{dx}\left(x+4\right), a/b=\frac{1}{7}, f=\left(x+4\right)^2, c/f=\frac{\frac{d}{dx}\left(x-6\right)\left(x+4\right)-\left(x-6\right)\frac{d}{dx}\left(x+4\right)}{\left(x+4\right)^2} e a/bc/f=\frac{1}{7}\sqrt[7]{\left(\frac{x+4}{x-6}\right)^{6}}\frac{\frac{d}{dx}\left(x-6\right)\left(x+4\right)-\left(x-6\right)\frac{d}{dx}\left(x+4\right)}{\left(x+4\right)^2}.
d/dx(((x-6)/(x+4))^(1/7))
Risposta finale al problema
$\frac{x+4-x+6}{7\left(x+4\right)^2}\sqrt[7]{\left(\frac{x+4}{x-6}\right)^{6}}$