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$$$2 n - 1$$$ 的導數
您的輸入
求$$$\frac{d}{dn} \left(2 n - 1\right)$$$。
解答
和/差的導數等於導數的和/差：
$${\color{red}\left(\frac{d}{dn} \left(2 n - 1\right)\right)} = {\color{red}\left(\frac{d}{dn} \left(2 n\right) - \frac{d}{dn} \left(1\right)\right)}$$常數的導數為$$$0$$$：
$$- {\color{red}\left(\frac{d}{dn} \left(1\right)\right)} + \frac{d}{dn} \left(2 n\right) = - {\color{red}\left(0\right)} + \frac{d}{dn} \left(2 n\right)$$套用常數倍法則 $$$\frac{d}{dn} \left(c f{\left(n \right)}\right) = c \frac{d}{dn} \left(f{\left(n \right)}\right)$$$，使用 $$$c = 2$$$ 與 $$$f{\left(n \right)} = n$$$：
$${\color{red}\left(\frac{d}{dn} \left(2 n\right)\right)} = {\color{red}\left(2 \frac{d}{dn} \left(n\right)\right)}$$套用冪次法則 $$$\frac{d}{dn} \left(n^{m}\right) = m n^{m - 1}$$$，取 $$$m = 1$$$，也就是 $$$\frac{d}{dn} \left(n\right) = 1$$$：
$$2 {\color{red}\left(\frac{d}{dn} \left(n\right)\right)} = 2 {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dn} \left(2 n - 1\right) = 2$$$。
答案
$$$\frac{d}{dn} \left(2 n - 1\right) = 2$$$A
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