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