Risolvere: $\frac{d}{dx}\left(x^x\sqrt[7]{\left(x^7+6\right)\left(x-6\right)^7}\right)$
Esercizio
$\frac{dy}{dx}\left(x^x\right)\sqrt[7]{\left(x^7+6\right)\left(x-6\right)^7}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x^x((x^7+6)(x-6)^7)^(1/7)). Applicare la formula: \left(ab\right)^n=a^nb^n. Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=x^x\sqrt[7]{x^7+6}\left(x-6\right), a=x^x, b=\sqrt[7]{x^7+6}\left(x-6\right) e d/dx?ab=\frac{d}{dx}\left(x^x\sqrt[7]{x^7+6}\left(x-6\right)\right). Applicare la formula: \frac{d}{dx}\left(ab\right)=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right), dove d/dx=\frac{d}{dx}, ab=\sqrt[7]{x^7+6}\left(x-6\right), a=\sqrt[7]{x^7+6}, b=x-6 e d/dx?ab=\frac{d}{dx}\left(\sqrt[7]{x^7+6}\left(x-6\right)\right). 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=x^7+6.
d/dx(x^x((x^7+6)(x-6)^7)^(1/7))
Risposta finale al problema
$\left(\ln\left(x\right)+1\right)x^x\sqrt[7]{x^7+6}\left(x-6\right)+\frac{x^{\left(x+6\right)}\left(x-6\right)}{\sqrt[7]{\left(x^7+6\right)^{6}}}+x^x\sqrt[7]{x^7+6}$