Risolvere: $\frac{d}{dx}\left(\ln\left(x^3+2\right)^2\ln\left(x^5+4\right)^4\right)$
Esercizio
$\frac{dy}{dx}\left(ln\left(x^3\:+\:2\right)^2ln\left(x^5\:+\:4\right)^4\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di espressioni algebriche passo dopo passo. d/dx(ln(x^3+2)^2ln(x^5+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=\ln\left(x^3+2\right)^2\ln\left(x^5+4\right)^4, a=\ln\left(x^3+2\right)^2, b=\ln\left(x^5+4\right)^4 e d/dx?ab=\frac{d}{dx}\left(\ln\left(x^3+2\right)^2\ln\left(x^5+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=\ln\left(x^3+2\right). 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=\ln\left(x^5+4\right). Applicare la formula: x^1=x.
d/dx(ln(x^3+2)^2ln(x^5+4)^4)
Risposta finale al problema
$\frac{6x^{2}\ln\left(x^5+4\right)^4\ln\left(x^3+2\right)}{x^3+2}+\frac{20\ln\left(x^3+2\right)^2\ln\left(x^5+4\right)^{3}x^{4}}{x^5+4}$