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$$$x^{3}$$$ 的二阶导数
您的输入
求$$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right)$$$。
解答
求一阶导数 $$$\frac{d}{dx} \left(x^{3}\right)$$$
应用幂次法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，其中 $$$n = 3$$$:
$${\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} = {\color{red}\left(3 x^{2}\right)}$$因此，$$$\frac{d}{dx} \left(x^{3}\right) = 3 x^{2}$$$。
接下来，$$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = \frac{d}{dx} \left(3 x^{2}\right)$$$
对 $$$c = 3$$$ 和 $$$f{\left(x \right)} = x^{2}$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(3 x^{2}\right)\right)} = {\color{red}\left(3 \frac{d}{dx} \left(x^{2}\right)\right)}$$应用幂次法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，其中 $$$n = 2$$$:
$$3 {\color{red}\left(\frac{d}{dx} \left(x^{2}\right)\right)} = 3 {\color{red}\left(2 x\right)}$$因此，$$$\frac{d}{dx} \left(3 x^{2}\right) = 6 x$$$。
因此，$$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = 6 x$$$。
答案
$$$\frac{d^{2}}{dx^{2}} \left(x^{3}\right) = 6 x$$$A
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