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