Esercizio
$\frac{d}{dx}\left(x^x\right)log2\left(x\:+\:6\right)$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. d/dx(x^xlog2(x+6)). 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\log_{2}\left(x+6\right), a=x^x, b=\log_{2}\left(x+6\right) e d/dx?ab=\frac{d}{dx}\left(x^x\log_{2}\left(x+6\right)\right). Applicare la formula: \frac{d}{dx}\left(\log_{a}\left(x\right)\right)=\frac{d}{dx}\left(\frac{\ln\left(x\right)}{\ln\left(a\right)}\right), dove a=2 e x=x+6. Applicare la formula: \frac{d}{dx}\left(\frac{x}{c}\right)=\frac{1}{c}\frac{d}{dx}\left(x\right), dove c=\ln\left(2\right) e x=\ln\left(x+6\right). Applicare la formula: \frac{d}{dx}\left(\ln\left(x\right)\right)=\frac{1}{x}\frac{d}{dx}\left(x\right).
Risposta finale al problema
$\left(\ln\left(x\right)+1\right)x^x\log_{2}\left(x+6\right)+\frac{x^x}{\ln\left(2\right)\left(x+6\right)}$