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