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Afgeleide van $$$\frac{\cos{\left(t \right)}}{3}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)$$$.
Oplossing
Pas de regel van de constante factor $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ toe met $$$c = \frac{1}{3}$$$ en $$$f{\left(t \right)} = \cos{\left(t \right)}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dt} \left(\cos{\left(t \right)}\right)}{3}\right)}$$De afgeleide van de cosinus is $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:
$$\frac{{\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)}}{3} = \frac{{\color{red}\left(- \sin{\left(t \right)}\right)}}{3}$$Dus, $$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$.
Antwoord
$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$A