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

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

Applicare la formula: $\frac{d}{dx}\left(\arcsin\left(\theta \right)\right)$$=\frac{1}{\sqrt{1-\theta ^2}}\frac{d}{dx}\left(\theta \right)$

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