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