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$$$\frac{5}{x}$$$의 도함수
사용자 입력
$$$\frac{d}{dx} \left(\frac{5}{x}\right)$$$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 $$$c = 5$$$와 $$$f{\left(x \right)} = \frac{1}{x}$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(\frac{5}{x}\right)\right)} = {\color{red}\left(5 \frac{d}{dx} \left(\frac{1}{x}\right)\right)}$$거듭제곱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = -1$$$에 적용합니다:
$$5 {\color{red}\left(\frac{d}{dx} \left(\frac{1}{x}\right)\right)} = 5 {\color{red}\left(- \frac{1}{x^{2}}\right)}$$따라서, $$$\frac{d}{dx} \left(\frac{5}{x}\right) = - \frac{5}{x^{2}}$$$.
정답
$$$\frac{d}{dx} \left(\frac{5}{x}\right) = - \frac{5}{x^{2}}$$$A
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