Afgeleide van $$$\frac{\sqrt{6} \sin{\left(v \right)}}{6}$$$
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Uw invoer
Bepaal $$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right)$$$.
Oplossing
Pas de regel van de constante factor $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$ toe met $$$c = \frac{\sqrt{6}}{6}$$$ en $$$f{\left(v \right)} = \sin{\left(v \right)}$$$:
$${\color{red}\left(\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right)\right)} = {\color{red}\left(\frac{\sqrt{6}}{6} \frac{d}{dv} \left(\sin{\left(v \right)}\right)\right)}$$De afgeleide van de sinus is $$$\frac{d}{dv} \left(\sin{\left(v \right)}\right) = \cos{\left(v \right)}$$$:
$$\frac{\sqrt{6} {\color{red}\left(\frac{d}{dv} \left(\sin{\left(v \right)}\right)\right)}}{6} = \frac{\sqrt{6} {\color{red}\left(\cos{\left(v \right)}\right)}}{6}$$Dus, $$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right) = \frac{\sqrt{6} \cos{\left(v \right)}}{6}$$$.
Antwoord
$$$\frac{d}{dv} \left(\frac{\sqrt{6} \sin{\left(v \right)}}{6}\right) = \frac{\sqrt{6} \cos{\left(v \right)}}{6}$$$A