Aprenda online a resolver problemas passo a passo. d/dx(((x(x-4))/(x^2+6))^(1/7)). Aplicamos a regra: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), onde a=\frac{1}{7} e x=\frac{x\left(x-4\right)}{x^2+6}. Aplicamos a regra: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, onde a=x\left(x-4\right), b=x^2+6 e n=-\frac{6}{7}. Aplicamos a regra: \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}, onde a=x\left(x-4\right) e b=x^2+6. Aplicamos a regra: \frac{a}{b}\frac{c}{f}=\frac{ac}{bf}, onde a=1, b=7, c=\frac{d}{dx}\left(x\left(x-4\right)\right)\left(x^2+6\right)-x\left(x-4\right)\frac{d}{dx}\left(x^2+6\right), a/b=\frac{1}{7}, f=\left(x^2+6\right)^2, c/f=\frac{\frac{d}{dx}\left(x\left(x-4\right)\right)\left(x^2+6\right)-x\left(x-4\right)\frac{d}{dx}\left(x^2+6\right)}{\left(x^2+6\right)^2} e a/bc/f=\frac{1}{7}\sqrt[7]{\left(\frac{x^2+6}{x\left(x-4\right)}\right)^{6}}\frac{\frac{d}{dx}\left(x\left(x-4\right)\right)\left(x^2+6\right)-x\left(x-4\right)\frac{d}{dx}\left(x^2+6\right)}{\left(x^2+6\right)^2}.

d/dx(((x(x-4))/(x^2+6))^(1/7))