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Tweede afgeleide van $$$\cosh{\left(x \right)}$$$
Gerelateerde rekenmachines: Afgeleide rekenmachine, Rekenmachine voor logaritmisch differentiëren
Uw invoer
Bepaal $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right)$$$.
Oplossing
Bepaal de eerste afgeleide $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right)$$$
De afgeleide van de hyperbolische cosinus is $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\cosh{\left(x \right)}\right)\right)} = {\color{red}\left(\sinh{\left(x \right)}\right)}$$Dus, $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$.
Vervolgens, $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \frac{d}{dx} \left(\sinh{\left(x \right)}\right)$$$
De afgeleide van de hyperbolische sinus is $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sinh{\left(x \right)}\right)\right)} = {\color{red}\left(\cosh{\left(x \right)}\right)}$$Dus, $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$.
Daarom geldt $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$.
Antwoord
$$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$A