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Afgeleide van $$$2 \sin{\left(t \right)}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right)$$$.
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 $$$c = 2$$$ en $$$f{\left(t \right)} = \sin{\left(t \right)}$$$:
$${\color{red}\left(\frac{d}{dt} \left(2 \sin{\left(t \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}$$De afgeleide van de sinus is $$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)} = 2 {\color{red}\left(\cos{\left(t \right)}\right)}$$Dus, $$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right) = 2 \cos{\left(t \right)}$$$.
Antwoord
$$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right) = 2 \cos{\left(t \right)}$$$A