$$$3 \sin{\left(x \right)} - 2$$$의 도함수

합/차의 도함수는 도함수들의 합/차이다:

$${\color{red}\left(\frac{d}{dx} \left(3 \sin{\left(x \right)} - 2\right)\right)} = {\color{red}\left(\frac{d}{dx} \left(3 \sin{\left(x \right)}\right) - \frac{d}{dx} \left(2\right)\right)}$$

상수의 도함수는 $$$0$$$입니다:

$$- {\color{red}\left(\frac{d}{dx} \left(2\right)\right)} + \frac{d}{dx} \left(3 \sin{\left(x \right)}\right) = - {\color{red}\left(0\right)} + \frac{d}{dx} \left(3 \sin{\left(x \right)}\right)$$

상수배 법칙 $$$\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$$$을 $$$c = 3$$$와 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$에 적용합니다:

$${\color{red}\left(\frac{d}{dx} \left(3 \sin{\left(x \right)}\right)\right)} = {\color{red}\left(3 \frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)}$$

사인 함수의 도함수는 $$$\frac{d}{dx} \left(\sin{\left(x \right)}\right) = \cos{\left(x \right)}$$$:

$$3 {\color{red}\left(\frac{d}{dx} \left(\sin{\left(x \right)}\right)\right)} = 3 {\color{red}\left(\cos{\left(x \right)}\right)}$$

따라서, $$$\frac{d}{dx} \left(3 \sin{\left(x \right)} - 2\right) = 3 \cos{\left(x \right)}$$$.