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