Bestimme $$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right)$$$
Ähnliche Rechner: Rechner für logarithmische Differentiation, Rechner zur impliziten Differentiation mit Schritten
Ihre Eingabe
Bestimme $$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right)$$$.
Lösung
Bestimme die erste Ableitung $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right)$$$
Die Ableitung des Sinus ist $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = {\color{red}\left(\cos{\left(x \right)}\right)}$$Somit gilt $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$.
Als Nächstes, $$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = \frac{d}{dx} \left(\cos{\left(x \right)}\right)$$$
Die Ableitung des Kosinus ist $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = {\color{red}\left(- \sin{\left(x \right)}\right)}$$Somit gilt $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$.
Daher $$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = - \sin{\left(x \right)}$$$.
Antwort
$$$\frac{d^{2}}{dx^{2}} \left(\sin{\left(x \right)}\right) = - \sin{\left(x \right)}$$$A