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$$$4 t^{2}$$$的导数
您的输入
求$$$\frac{d}{dt} \left(4 t^{2}\right)$$$。
解答
对 $$$c = 4$$$ 和 $$$f{\left(t \right)} = t^{2}$$$ 应用常数倍法则 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$：
$${\color{red}\left(\frac{d}{dt} \left(4 t^{2}\right)\right)} = {\color{red}\left(4 \frac{d}{dt} \left(t^{2}\right)\right)}$$应用幂次法则 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$，其中 $$$n = 2$$$:
$$4 {\color{red}\left(\frac{d}{dt} \left(t^{2}\right)\right)} = 4 {\color{red}\left(2 t\right)}$$因此，$$$\frac{d}{dt} \left(4 t^{2}\right) = 8 t$$$。
答案
$$$\frac{d}{dt} \left(4 t^{2}\right) = 8 t$$$A
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