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$$$\sqrt{2} \sqrt{t}$$$の導関数
入力内容
$$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ を $$$c = \sqrt{2}$$$ と $$$f{\left(t \right)} = \sqrt{t}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right)\right)} = {\color{red}\left(\sqrt{2} \frac{d}{dt} \left(\sqrt{t}\right)\right)}$$冪法則 $$$\frac{d}{dt} \left(t^{n}\right) = n t^{n - 1}$$$ を $$$n = \frac{1}{2}$$$ に対して適用する:
$$\sqrt{2} {\color{red}\left(\frac{d}{dt} \left(\sqrt{t}\right)\right)} = \sqrt{2} {\color{red}\left(\frac{1}{2 \sqrt{t}}\right)}$$したがって、$$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$。
解答
$$$\frac{d}{dt} \left(\sqrt{2} \sqrt{t}\right) = \frac{\sqrt{2}}{2 \sqrt{t}}$$$A
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