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Segunda derivada de $$$\cosh{\left(x \right)}$$$
Calculadoras relacionadas: Calculadora de derivadas, Calculadora de diferenciación logarítmica
Tu entrada
Halla $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right)$$$.
Solución
Calcule la primera derivada $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right)$$$
La derivada del coseno hiperbólico es $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\cosh{\left(x \right)}\right)\right)} = {\color{red}\left(\sinh{\left(x \right)}\right)}$$Por lo tanto, $$$\frac{d}{dx} \left(\cosh{\left(x \right)}\right) = \sinh{\left(x \right)}$$$.
A continuación, $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \frac{d}{dx} \left(\sinh{\left(x \right)}\right)$$$
La derivada del seno hiperbólico es $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(\sinh{\left(x \right)}\right)\right)} = {\color{red}\left(\cosh{\left(x \right)}\right)}$$Por lo tanto, $$$\frac{d}{dx} \left(\sinh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$.
Por lo tanto, $$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$.
Respuesta
$$$\frac{d^{2}}{dx^{2}} \left(\cosh{\left(x \right)}\right) = \cosh{\left(x \right)}$$$A