$$$\frac{\sqrt{7} \sin{\left(u \right)}}{7}$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$，使用 $$$c = \frac{\sqrt{7}}{7}$$$ 與 $$$f{\left(u \right)} = \sin{\left(u \right)}$$$：
$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)\right)} = {\color{red}\left(\frac{\sqrt{7}}{7} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$正弦函數的導數為$$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$：
$$\frac{\sqrt{7} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{7} = \frac{\sqrt{7} {\color{red}\left(\cos{\left(u \right)}\right)}}{7}$$因此，$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$。
答案
$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$A