Impara online a risolvere i problemi di limiti all'infinito passo dopo passo. d/dx(((cos(2x)^4)/((x^3-8)^2))^(1/3)). 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}{3} e x=\frac{\cos\left(2x\right)^4}{\left(x^3-8\right)^2}. Applicare la formula: \left(\frac{a}{b}\right)^n=\left(\frac{b}{a}\right)^{\left|n\right|}, dove a=\cos\left(2x\right)^4, b=\left(x^3-8\right)^2 e n=-\frac{2}{3}. 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=\cos\left(2x\right)^4 e b=\left(x^3-8\right)^2. Simplify \left(\left(x^3-8\right)^2\right)^2 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 2.

d/dx(((cos(2x)^4)/((x^3-8)^2))^(1/3))