$$$2 u \cos{\left(5 v \right)}$$$ 关于 $$$u$$$ 的导数
您的输入
求$$$\frac{d}{du} \left(2 u \cos{\left(5 v \right)}\right)$$$。
解答
对 $$$c = 2 \cos{\left(5 v \right)}$$$ 和 $$$f{\left(u \right)} = u$$$ 应用常数倍法则 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$：
$${\color{red}\left(\frac{d}{du} \left(2 u \cos{\left(5 v \right)}\right)\right)} = {\color{red}\left(2 \cos{\left(5 v \right)} \frac{d}{du} \left(u\right)\right)}$$应用幂法则 $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{du} \left(u\right) = 1$$$：
$$2 \cos{\left(5 v \right)} {\color{red}\left(\frac{d}{du} \left(u\right)\right)} = 2 \cos{\left(5 v \right)} {\color{red}\left(1\right)}$$因此，$$$\frac{d}{du} \left(2 u \cos{\left(5 v \right)}\right) = 2 \cos{\left(5 v \right)}$$$。
答案
$$$\frac{d}{du} \left(2 u \cos{\left(5 v \right)}\right) = 2 \cos{\left(5 v \right)}$$$A
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