|
|
|
|
|
|
|
|
|
|
|
|
Derivada de $$$- \csc{\left(x \right)}$$$
Calculadoras relacionadas: Calculadora de diferenciación logarítmica, Calculadora de derivación implícita con pasos
Tu entrada
Halla $$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right)$$$.
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 $$$c = -1$$$ y $$$f{\left(x \right)} = \csc{\left(x \right)}$$$:
$${\color{red}\left(\frac{d}{dx} \left(- \csc{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\csc{\left(x \right)}\right)\right)}$$La derivada de la cosecante es $$$\frac{d}{dx} \left(\csc{\left(x \right)}\right) = - \cot{\left(x \right)} \csc{\left(x \right)}$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(\csc{\left(x \right)}\right)\right)} = - {\color{red}\left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)}$$Por lo tanto, $$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right) = \cot{\left(x \right)} \csc{\left(x \right)}$$$.
Respuesta
$$$\frac{d}{dx} \left(- \csc{\left(x \right)}\right) = \cot{\left(x \right)} \csc{\left(x \right)}$$$A