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Afgeleide van $$$\frac{\sqrt{5} \cosh{\left(u \right)}}{2}$$$
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Uw invoer
Bepaal $$$\frac{d}{du} \left(\frac{\sqrt{5} \cosh{\left(u \right)}}{2}\right)$$$.
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 $$$c = \frac{\sqrt{5}}{2}$$$ en $$$f{\left(u \right)} = \cosh{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{5} \cosh{\left(u \right)}}{2}\right)\right)} = {\color{red}\left(\frac{\sqrt{5}}{2} \frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}$$De afgeleide van de hyperbolische cosinus is $$$\frac{d}{du} \left(\cosh{\left(u \right)}\right) = \sinh{\left(u \right)}$$$:
$$\frac{\sqrt{5} {\color{red}\left(\frac{d}{du} \left(\cosh{\left(u \right)}\right)\right)}}{2} = \frac{\sqrt{5} {\color{red}\left(\sinh{\left(u \right)}\right)}}{2}$$Dus, $$$\frac{d}{du} \left(\frac{\sqrt{5} \cosh{\left(u \right)}}{2}\right) = \frac{\sqrt{5} \sinh{\left(u \right)}}{2}$$$.
Antwoord
$$$\frac{d}{du} \left(\frac{\sqrt{5} \cosh{\left(u \right)}}{2}\right) = \frac{\sqrt{5} \sinh{\left(u \right)}}{2}$$$A