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Afgeleide van $$$\sqrt{2} \sqrt{t}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)$$$.
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 $$$c = \sqrt{2}$$$ en $$$f{\left(t \right)} = \sqrt{t}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)\right)} = {\color{red}\left(\sqrt{2} \frac{d}{dt} \left(\sqrt{t}\right)\right)}$$Pas de machtsregel $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ toe met $$$n = \frac{1}{2}$$$:
$$\sqrt{2} {\color{red}\left(\frac{d}{dt} \left(\sqrt{t}\right)\right)} = \sqrt{2} {\color{red}\left(\frac{1}{2 \sqrt{t}}\right)}$$Dus, $$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$.
Antwoord
$$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$A