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