Derivada de $$$2 \operatorname{atan}{\left(v \right)}$$$
Calculadoras relacionadas: Calculadora de diferenciación logarítmica, Calculadora de derivación implícita con pasos
Tu entrada
Halla $$$\frac{d}{dv} \left(2 \operatorname{atan}{\left(v \right)}\right)$$$.
Solución
Aplica la regla del factor constante $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$ con $$$c = 2$$$ y $$$f{\left(v \right)} = \operatorname{atan}{\left(v \right)}$$$:
$${\color{red}\left(\frac{d}{dv} \left(2 \operatorname{atan}{\left(v \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right)\right)}$$La derivada de la arctangente es $$$\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right) = \frac{1}{v^{2} + 1}$$$:
$$2 {\color{red}\left(\frac{d}{dv} \left(\operatorname{atan}{\left(v \right)}\right)\right)} = 2 {\color{red}\left(\frac{1}{v^{2} + 1}\right)}$$Por lo tanto, $$$\frac{d}{dv} \left(2 \operatorname{atan}{\left(v \right)}\right) = \frac{2}{v^{2} + 1}$$$.
Respuesta
$$$\frac{d}{dv} \left(2 \operatorname{atan}{\left(v \right)}\right) = \frac{2}{v^{2} + 1}$$$A