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$$$2 x^{3}$$$의 도함수
사용자 입력
$$$\frac{d}{dx} \left(2 x^{3}\right)$$$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 $$$c = 2$$$와 $$$f{\left(x \right)} = x^{3}$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(2 x^{3}\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(x^{3}\right)\right)}$$거듭제곱법칙 $$$\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$$$을 $$$n = 3$$$에 적용합니다:
$$2 {\color{red}\left(\frac{d}{dx} \left(x^{3}\right)\right)} = 2 {\color{red}\left(3 x^{2}\right)}$$따라서, $$$\frac{d}{dx} \left(2 x^{3}\right) = 6 x^{2}$$$.
정답
$$$\frac{d}{dx} \left(2 x^{3}\right) = 6 x^{2}$$$A
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