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Afgeleide van $$$\frac{\sqrt{2} x}{4}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)$$$.
Oplossing
Pas de regel van de constante factor $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ toe met $$$c = \frac{\sqrt{2}}{4}$$$ en $$$f{\left(x \right)} = x$$$:
$${\color{red}\left(\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)\right)} = {\color{red}\left(\frac{\sqrt{2}}{4} \frac{d}{dx} \left(x\right)\right)}$$Pas de machtsregel $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ toe met $$$n = 1$$$, met andere woorden, $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$\frac{\sqrt{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{4} = \frac{\sqrt{2} {\color{red}\left(1\right)}}{4}$$Dus, $$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$.
Antwoord
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$A