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$$$\frac{\pi t}{2}$$$ 的導數
您的輸入
求$$$\frac{d}{dt} \left(\frac{\pi t}{2}\right)$$$。
解答
套用常數倍法則 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$，使用 $$$c = \frac{\pi}{2}$$$ 與 $$$f{\left(t \right)} = t$$$：
$${\color{red}\left(\frac{d}{dt} \left(\frac{\pi t}{2}\right)\right)} = {\color{red}\left(\frac{\pi}{2} \frac{d}{dt} \left(t\right)\right)}$$套用冪次法則 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$，取 $$$n = 1$$$，也就是 $$$\frac{d}{dt} \left(t\right) = 1$$$：
$$\frac{\pi {\color{red}\left(\frac{d}{dt} \left(t\right)\right)}}{2} = \frac{\pi {\color{red}\left(1\right)}}{2}$$因此，$$$\frac{d}{dt} \left(\frac{\pi t}{2}\right) = \frac{\pi}{2}$$$。
答案
$$$\frac{d}{dt} \left(\frac{\pi t}{2}\right) = \frac{\pi}{2}$$$A
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