$$$\frac{u}{4}$$$ 的導數
您的輸入
求$$$\frac{d}{du} \left(\frac{u}{4}\right)$$$。
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 $$$c = \frac{1}{4}$$$ 與 $$$f{\left(u \right)} = u$$$：
$${\color{red}\left(\frac{d}{du} \left(\frac{u}{4}\right)\right)} = {\color{red}\left(\frac{\frac{d}{du} \left(u\right)}{4}\right)}$$套用冪次法則 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{du} \left(u\right) = 1$$$：
$$\frac{{\color{red}\left(\frac{d}{du} \left(u\right)\right)}}{4} = \frac{{\color{red}\left(1\right)}}{4}$$因此，$$$\frac{d}{du} \left(\frac{u}{4}\right) = \frac{1}{4}$$$。
答案
$$$\frac{d}{du} \left(\frac{u}{4}\right) = \frac{1}{4}$$$A