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$$$r \cos{\left(\theta \right)}$$$ 對 $$$r$$$ 的導數
您的輸入
求$$$\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dr} \left(c f{\left(r \right)}\right) = c \frac{d}{dr} \left(f{\left(r \right)}\right)$$$，使用 $$$c = \cos{\left(\theta \right)}$$$ 與 $$$f{\left(r \right)} = r$$$：
$${\color{red}\left(\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right)\right)} = {\color{red}\left(\cos{\left(\theta \right)} \frac{d}{dr} \left(r\right)\right)}$$套用冪次法則 $$$\frac{d}{dr} \left(r^{n}\right) = n r^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dr} \left(r\right) = 1$$$：
$$\cos{\left(\theta \right)} {\color{red}\left(\frac{d}{dr} \left(r\right)\right)} = \cos{\left(\theta \right)} {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right) = \cos{\left(\theta \right)}$$$。
答案
$$$\frac{d}{dr} \left(r \cos{\left(\theta \right)}\right) = \cos{\left(\theta \right)}$$$A
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