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$$$1 - 4 v^{2}$$$的导数
您的输入
求$$$\frac{d}{dv} \left(1 - 4 v^{2}\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dv} \left(1 - 4 v^{2}\right)\right)} = {\color{red}\left(\frac{d}{dv} \left(1\right) - \frac{d}{dv} \left(4 v^{2}\right)\right)}$$常数的导数是$$$0$$$:
$${\color{red}\left(\frac{d}{dv} \left(1\right)\right)} - \frac{d}{dv} \left(4 v^{2}\right) = {\color{red}\left(0\right)} - \frac{d}{dv} \left(4 v^{2}\right)$$对 $$$c = 4$$$ 和 $$$f{\left(v \right)} = v^{2}$$$ 应用常数倍法则 $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$：
$$- {\color{red}\left(\frac{d}{dv} \left(4 v^{2}\right)\right)} = - {\color{red}\left(4 \frac{d}{dv} \left(v^{2}\right)\right)}$$应用幂次法则 $$$\frac{d}{dv} \left(v^{n}\right) = n v^{n - 1}$$$，其中 $$$n = 2$$$:
$$- 4 {\color{red}\left(\frac{d}{dv} \left(v^{2}\right)\right)} = - 4 {\color{red}\left(2 v\right)}$$因此，$$$\frac{d}{dv} \left(1 - 4 v^{2}\right) = - 8 v$$$。
答案
$$$\frac{d}{dv} \left(1 - 4 v^{2}\right) = - 8 v$$$A
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