Esercizio
$\frac{d}{dx}\left(x^x\right)\left(x^5\:+\:2\right)^2\left(x^4\:+\:4\right)^4$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x^x(x^5+2)^2(x^4+4)^4). 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\left(x^5+2\right)^2\left(x^4+4\right)^4, a=x^x, b=\left(x^5+2\right)^2\left(x^4+4\right)^4 e d/dx?ab=\frac{d}{dx}\left(x^x\left(x^5+2\right)^2\left(x^4+4\right)^4\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=\left(x^5+2\right)^2\left(x^4+4\right)^4, a=\left(x^5+2\right)^2, b=\left(x^4+4\right)^4 e d/dx?ab=\frac{d}{dx}\left(\left(x^5+2\right)^2\left(x^4+4\right)^4\right). Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=2 e x=x^5+2. Applicare la formula: \frac{d}{dx}\left(x^a\right)=ax^{\left(a-1\right)}\frac{d}{dx}\left(x\right), dove a=4 e x=x^4+4.
d/dx(x^x(x^5+2)^2(x^4+4)^4)
Risposta finale al problema
$\left(\ln\left(x\right)+1\right)x^x\left(x^5+2\right)^2\left(x^4+4\right)^4+x^x\left(10\left(x^5+2\right)x^{4}\left(x^4+4\right)^4+16\left(x^5+2\right)^2\left(x^4+4\right)^{3}x^{3}\right)$