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$$$- \frac{\sin{\left(t \right)}}{2}$$$ 的導數
您的輸入
求$$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right)$$$。
解答
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 $$$f{\left(t \right)} = \sin{\left(t \right)}$$$：
$${\color{red}\left(\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right)\right)} = {\color{red}\left(- \frac{\frac{d}{dt} \left(\sin{\left(t \right)}\right)}{2}\right)}$$正弦函數的導數為$$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$：
$$- \frac{{\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}}{2} = - \frac{{\color{red}\left(\cos{\left(t \right)}\right)}}{2}$$因此，$$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right) = - \frac{\cos{\left(t \right)}}{2}$$$。
答案
$$$\frac{d}{dt} \left(- \frac{\sin{\left(t \right)}}{2}\right) = - \frac{\cos{\left(t \right)}}{2}$$$A
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