$$$1 - \frac{\sin{\left(t \right)}}{2}$$$ 的導數

和/差的導數等於導數的和/差：

$${\color{red}\left(\frac{d}{dt} \left(1 - \frac{\sin{\left(t \right)}}{2}\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(1\right) - \frac{d}{dt} \left(\frac{\sin{\left(t \right)}}{2}\right)\right)}$$

套用常數倍法則 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$，使用 $$$c = \frac{1}{2}$$$ 與 $$$f{\left(t \right)} = \sin{\left(t \right)}$$$：

$$- {\color{red}\left(\frac{d}{dt} \left(\frac{\sin{\left(t \right)}}{2}\right)\right)} + \frac{d}{dt} \left(1\right) = - {\color{red}\left(\frac{\frac{d}{dt} \left(\sin{\left(t \right)}\right)}{2}\right)} + \frac{d}{dt} \left(1\right)$$

正弦函數的導數為$$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$：

$$- \frac{{\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}}{2} + \frac{d}{dt} \left(1\right) = - \frac{{\color{red}\left(\cos{\left(t \right)}\right)}}{2} + \frac{d}{dt} \left(1\right)$$

常數的導數為$$$0$$$：

$$- \frac{\cos{\left(t \right)}}{2} + {\color{red}\left(\frac{d}{dt} \left(1\right)\right)} = - \frac{\cos{\left(t \right)}}{2} + {\color{red}\left(0\right)}$$

因此，$$$\frac{d}{dt} \left(1 - \frac{\sin{\left(t \right)}}{2}\right) = - \frac{\cos{\left(t \right)}}{2}$$$。