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