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$$$\frac{\sqrt{2} x}{4}$$$의 도함수
사용자 입력
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)$$$을(를) 구하시오.
풀이
상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = \frac{\sqrt{2}}{4}$$$와 $$$f{\left(x \right)} = x$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right)\right)} = {\color{red}\left(\frac{\sqrt{2}}{4} \frac{d}{dx} \left(x\right)\right)}$$멱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = 1$$$에 대해 적용하면, 즉 $$$\frac{d}{dx} \left(x\right) = 1$$$:
$$\frac{\sqrt{2} {\color{red}\left(\frac{d}{dx} \left(x\right)\right)}}{4} = \frac{\sqrt{2} {\color{red}\left(1\right)}}{4}$$따라서, $$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$.
정답
$$$\frac{d}{dx} \left(\frac{\sqrt{2} x}{4}\right) = \frac{\sqrt{2}}{4}$$$A
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