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Derivada de $$$\sin{\left(u \right)} \left|{a}\right|$$$ con respecto a $$$u$$$
Calculadoras relacionadas: Calculadora de diferenciación logarítmica, Calculadora de derivación implícita con pasos
Tu entrada
Halla $$$\frac{d}{du} \left(\sin{\left(u \right)} \left|{a}\right|\right)$$$.
Solución
Aplica la regla del factor constante $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ con $$$c = \left|{a}\right|$$$ y $$$f{\left(u \right)} = \sin{\left(u \right)}$$$:
$${\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)} \left|{a}\right|\right)\right)} = {\color{red}\left(\left|{a}\right| \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$La derivada del seno es $$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\left|{a}\right| {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)} = \left|{a}\right| {\color{red}\left(\cos{\left(u \right)}\right)}$$Por lo tanto, $$$\frac{d}{du} \left(\sin{\left(u \right)} \left|{a}\right|\right) = \cos{\left(u \right)} \left|{a}\right|$$$.
Respuesta
$$$\frac{d}{du} \left(\sin{\left(u \right)} \left|{a}\right|\right) = \cos{\left(u \right)} \left|{a}\right|$$$A