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Afgeleide van $$$\frac{\ln\left(x\right)}{\ln\left(2\right)}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)$$$.
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 $$$c = \frac{1}{\ln\left(2\right)}$$$ en $$$f{\left(x \right)} = \ln\left(x\right)$$$:
$${\color{red}\left(\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dx} \left(\ln\left(x\right)\right)}{\ln\left(2\right)}\right)}$$De afgeleide van de natuurlijke logaritme is $$$\frac{d}{dx} \left(\ln\left(x\right)\right) = \frac{1}{x}$$$:
$$\frac{{\color{red}\left(\frac{d}{dx} \left(\ln\left(x\right)\right)\right)}}{\ln\left(2\right)} = \frac{{\color{red}\left(\frac{1}{x}\right)}}{\ln\left(2\right)}$$Dus, $$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$.
Antwoord
$$$\frac{d}{dx} \left(\frac{\ln\left(x\right)}{\ln\left(2\right)}\right) = \frac{1}{x \ln\left(2\right)}$$$A