|
|
|
|
|
|
|
|
|
|
|
|
Afgeleide van $$$2 \cosh{\left(u \right)}$$$
Gerelateerde rekenmachines: Rekenmachine voor logaritmisch differentiëren, Rekenmachine voor impliciete differentiatie met stappen
Uw invoer
Bepaal $$$\frac{d}{du} \left(2 \cosh{\left(u \right)}\right)$$$.
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 $$$c = 2$$$ en $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(2 \cosh{\left(u \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}$$De afgeleide van de hyperbolische cosinus is $$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$:
$$2 {\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)} = 2 {\color{red}\left(\sinh{\left(u \right)}\right)}$$Dus, $$$\frac{d}{du} \left(2 \cosh{\left(u \right)}\right) = 2 \sinh{\left(u \right)}$$$.
Antwoord
$$$\frac{d}{du} \left(2 \cosh{\left(u \right)}\right) = 2 \sinh{\left(u \right)}$$$A