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