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$$$\frac{\cos{\left(t \right)}}{3}$$$ 的導數
您的輸入
求$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)$$$。
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 $$$c = \frac{1}{3}$$$ 與 $$$f{\left(t \right)} = \cos{\left(t \right)}$$$：
$${\color{red}\left(\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dt} \left(\cos{\left(t \right)}\right)}{3}\right)}$$餘弦函數的導數為 $$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$：
$$\frac{{\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)}}{3} = \frac{{\color{red}\left(- \sin{\left(t \right)}\right)}}{3}$$因此，$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$。
答案
$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$A
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