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$$$2 t - 4 u$$$ 关于 $$$t$$$ 的导数
您的输入
求$$$\frac{d}{dt} \left(2 t - 4 u\right)$$$。
解答
和/差的导数等于导数的和/差：
$${\color{red}\left(\frac{d}{dt} \left(2 t - 4 u\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(2 t\right) - \frac{d}{dt} \left(4 u\right)\right)}$$常数的导数是$$$0$$$:
$$- {\color{red}\left(\frac{d}{dt} \left(4 u\right)\right)} + \frac{d}{dt} \left(2 t\right) = - {\color{red}\left(0\right)} + \frac{d}{dt} \left(2 t\right)$$对 $$$c = 2$$$ 和 $$$f{\left(t \right)} = t$$$ 应用常数倍法则 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dt} \left(2 t\right)\right)} = {\color{red}\left(2 \frac{d}{dt} \left(t\right)\right)}$$应用幂法则 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$，取 $$$n = 1$$$，也就是说，$$$\frac{d}{dt} \left(t\right) = 1$$$：
$$2 {\color{red}\left(\frac{d}{dt} \left(t\right)\right)} = 2 {\color{red}\left(1\right)}$$因此，$$$\frac{d}{dt} \left(2 t - 4 u\right) = 2$$$。
答案
$$$\frac{d}{dt} \left(2 t - 4 u\right) = 2$$$A
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