Derivada de $$$x^{2} \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}$$$ con respecto a $$$x$$$
Calculadoras relacionadas: Calculadora de diferenciación logarítmica, Calculadora de derivación implícita con pasos
Tu entrada
Halla $$$\frac{d}{dx} \left(x^{2} \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}\right)$$$.
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 $$$c = \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}$$$ y $$$f{\left(x \right)} = x^{2}$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{2} \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}\right)\right)} = {\color{red}\left(\cos^{2}{\left(\tanh{\left(\eta \right)} \right)} \frac{d}{dx} \left(x^{2}\right)\right)}$$Aplica la regla de la potencia $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ con $$$n = 2$$$:
$$\cos^{2}{\left(\tanh{\left(\eta \right)} \right)} {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = \cos^{2}{\left(\tanh{\left(\eta \right)} \right)} {\color{red}\left(2 x\right)}$$Por lo tanto, $$$\frac{d}{dx} \left(x^{2} \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}\right) = 2 x \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}$$$.
Respuesta
$$$\frac{d}{dx} \left(x^{2} \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}\right) = 2 x \cos^{2}{\left(\tanh{\left(\eta \right)} \right)}$$$A