$$$6 u + v$$$ 关于 $$$u$$$ 的导数
您的输入
求$$$\frac{d}{du} \left(6 u + v\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{du} \left(6 u + v\right)\right)} = {\color{red}\left(\frac{d}{du} \left(6 u\right) + \frac{dv}{du}\right)}$$对 $$$c = 6$$$ 和 $$$f{\left(u \right)} = u$$$ 应用常数倍法则 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$：
$${\color{red}\left(\frac{d}{du} \left(6 u\right)\right)} + \frac{dv}{du} = {\color{red}\left(6 \frac{d}{du} \left(u\right)\right)} + \frac{dv}{du}$$应用幂法则 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{du} \left(u\right) = 1$$$：
$$6 {\color{red}\left(\frac{d}{du} \left(u\right)\right)} + \frac{dv}{du} = 6 {\color{red}\left(1\right)} + \frac{dv}{du}$$常数的导数是$$$0$$$:
$${\color{red}\left(\frac{dv}{du}\right)} + 6 = {\color{red}\left(0\right)} + 6$$因此，$$$\frac{d}{du} \left(6 u + v\right) = 6$$$。
答案
$$$\frac{d}{du} \left(6 u + v\right) = 6$$$A
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