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$$$2 x^{3} + 3$$$的导数
您的输入
求$$$\frac{d}{dx} \left(2 x^{3} + 3\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dx} \left(2 x^{3} + 3\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(2 x^{3}\right) + \frac{d}{dx} \left(3\right)\right)}$$对 $$$c = 2$$$ 和 $$$f{\left(x \right)} = x^{3}$$$ 应用常数倍法则 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dx} \left(2 x^{3}\right)\right)} + \frac{d}{dx} \left(3\right) = {\color{red}\left(2 \frac{d}{dx} \left(x^{3}\right)\right)} + \frac{d}{dx} \left(3\right)$$应用幂次法则 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$，其中 $$$n = 3$$$:
$$2 {\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} + \frac{d}{dx} \left(3\right) = 2 {\color{red}\left(3 x^{2}\right)} + \frac{d}{dx} \left(3\right)$$常数的导数是$$$0$$$:
$$6 x^{2} + {\color{red}\left(\frac{d}{dx} \left(3\right)\right)} = 6 x^{2} + {\color{red}\left(0\right)}$$因此，$$$\frac{d}{dx} \left(2 x^{3} + 3\right) = 6 x^{2}$$$。
答案
$$$\frac{d}{dx} \left(2 x^{3} + 3\right) = 6 x^{2}$$$A
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