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