$$$x \sin{\left(c \right)}$$$ 关于 $$$x$$$ 的导数
您的输入
求$$$\frac{d}{dx} \left(x \sin{\left(c \right)}\right)$$$。
解答
对 $$$k = \sin{\left(c \right)}$$$ 和 $$$f{\left(x \right)} = x$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(k f{\left(x \right)}\right) = k \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(x \sin{\left(c \right)}\right)\right)} = {\color{red}\left(\sin{\left(c \right)} \frac{d}{dx} \left(x\right)\right)}$$应用幂法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dx} \left(x\right) = 1$$$：
$$\sin{\left(c \right)} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = \sin{\left(c \right)} {\color{red}\left(1\right)}$$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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