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Derivada de $$$2 \sec{\left(x \right)}$$$
Calculadoras relacionadas: Calculadora de diferenciación logarítmica, Calculadora de derivación implícita con pasos
Tu entrada
Halla $$$\frac{d}{dx} \left(2 \sec{\left(x \right)}\right)$$$.
Solución
Aplica la regla del factor constante $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ con $$$c = 2$$$ y $$$f{\left(x \right)} = \sec{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(2 \sec{\left(x \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(\sec{\left(x \right)}\right)\right)}$$La derivada de la secante es $$$\frac{d}{dx} \left(\sec{\left(x \right)}\right) = \tan{\left(x \right)} \sec{\left(x \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dx} \left(\sec{\left(x \right)}\right)\right)} = 2 {\color{red}\left(\tan{\left(x \right)} \sec{\left(x \right)}\right)}$$Por lo tanto, $$$\frac{d}{dx} \left(2 \sec{\left(x \right)}\right) = 2 \tan{\left(x \right)} \sec{\left(x \right)}$$$.
Respuesta
$$$\frac{d}{dx} \left(2 \sec{\left(x \right)}\right) = 2 \tan{\left(x \right)} \sec{\left(x \right)}$$$A