$$$- c + c_{max}$$$ 對 $$$c$$$ 的導數
您的輸入
求$$$\frac{d}{dc} \left(- c + c_{max}\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dc} \left(- c + c_{max}\right)\right)} = {\color{red}\left(- \frac{d}{dc} \left(c\right) + \frac{dc_{max}}{dc}\right)}$$套用冪次法則 $$$\frac{d}{dc} \left(c^{n}\right) = n c^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dc} \left(c\right) = 1$$$：
$$- {\color{red}\left(\frac{d}{dc} \left(c\right)\right)} + \frac{dc_{max}}{dc} = - {\color{red}\left(1\right)} + \frac{dc_{max}}{dc}$$常數的導數為$$$0$$$：
$${\color{red}\left(\frac{dc_{max}}{dc}\right)} - 1 = {\color{red}\left(0\right)} - 1$$因此，$$$\frac{d}{dc} \left(- c + c_{max}\right) = -1$$$。
答案
$$$\frac{d}{dc} \left(- c + c_{max}\right) = -1$$$A
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