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