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$$$4 x$$$ 的二阶导数
您的输入
求$$$\frac{d^{2}}{dx^{2}} \left(4 x\right)$$$。
解答
求一阶导数 $$$\frac{d}{dx} \left(4 x\right)$$$
对 $$$c = 4$$$ 和 $$$f{\left(x \right)} = x$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(4 x\right)\right)} = {\color{red}\left(4 \frac{d}{dx} \left(x\right)\right)}$$应用幂法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dx} \left(x\right) = 1$$$：
$$4 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 4 {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dx} \left(4 x\right) = 4$$$。
接下来，$$$\frac{d^{2}}{dx^{2}} \left(4 x\right) = \frac{d}{dx} \left(4\right)$$$
常数的导数是$$$0$$$:
$${\color{red}\left(\frac{d}{dx} \left(4\right)\right)} = {\color{red}\left(0\right)}$$因此，$$$\frac{d}{dx} \left(4\right) = 0$$$。
因此，$$$\frac{d^{2}}{dx^{2}} \left(4 x\right) = 0$$$。
答案
$$$\frac{d^{2}}{dx^{2}} \left(4 x\right) = 0$$$A
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