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$$$\frac{\sqrt{2} x}{4}$$$の導関数
入力内容
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$ を $$$c = \frac{\sqrt{2}}{4}$$$ と $$$f{\left(x \right)} = x$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)\right)} = {\color{red}\left(\frac{\sqrt{2}}{4} \frac{d}{dx} \left(x\right)\right)}$$$$$n = 1$$$ を用いて冪法則 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$ を適用すると、すなわち $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$\frac{\sqrt{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{4} = \frac{\sqrt{2} {\color{red}\left(1\right)}}{4}$$したがって、$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$。
解答
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$A
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