$$$- \sin{\left(x \right)}$$$의 이차 도함수
사용자 입력
$$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right)$$$을(를) 구하시오.
풀이
제1도함수 $$$\frac{d}{dx} \left(- \sin{\left(x \right)}\right)$$$를 구하세요
상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = -1$$$와 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(- \sin{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)}$$사인 함수의 도함수는 $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:
$$- {\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = - {\color{red}\left(\cos{\left(x \right)}\right)}$$따라서, $$$\frac{d}{dx} \left(- \sin{\left(x \right)}\right) = - \cos{\left(x \right)}$$$.
다음으로, $$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \frac{d}{dx} \left(- \cos{\left(x \right)}\right)$$$
상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = -1$$$와 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$에 적용합니다:
$${\color{red}\left(\frac{d}{dx} \left(- \cos{\left(x \right)}\right)\right)} = {\color{red}\left(- \frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)}$$코사인의 도함수는 $$$\frac{d}{dx} \left(\cos{\left(x \right)}\right) = - \sin{\left(x \right)}$$$입니다:
$$- {\color{red}\left(\frac{d}{dx} \left(\cos{\left(x \right)}\right)\right)} = - {\color{red}\left(- \sin{\left(x \right)}\right)}$$따라서, $$$\frac{d}{dx} \left(- \cos{\left(x \right)}\right) = \sin{\left(x \right)}$$$.
따라서 $$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \sin{\left(x \right)}$$$.
정답
$$$\frac{d^{2}}{dx^{2}} \left(- \sin{\left(x \right)}\right) = \sin{\left(x \right)}$$$A