Applicare la formula: $\frac{d}{dx}\left(ab\right)$$=\frac{d}{dx}\left(a\right)b+a\frac{d}{dx}\left(b\right)$, dove $d/dx=\frac{d}{dx}$, $ab=x\cos\left(\ln\left(x\right)\right)$, $a=x$, $b=\cos\left(\ln\left(x\right)\right)$ e $d/dx?ab=\frac{d}{dx}\left(x\cos\left(\ln\left(x\right)\right)\right)$

Applicare la formula: $\frac{d}{dx}\left(x\right)$$=1$

Applicare l'identità trigonometrica: $\frac{d}{dx}\left(\cos\left(\theta \right)\right)$$=-\frac{d}{dx}\left(\theta \right)\sin\left(\theta \right)$, dove $x=\ln\left(x\right)$

Applicare la formula: $\frac{d}{dx}\left(\ln\left(x\right)\right)$$=\frac{1}{x}$