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$$$2 \sin{\left(t \right)}$$$の導関数
入力内容
$$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dt} \left(c f{\left(t \right)}\right) = c \frac{d}{dt} \left(f{\left(t \right)}\right)$$$ を $$$c = 2$$$ と $$$f{\left(t \right)} = \sin{\left(t \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dt} \left(2 \sin{\left(t \right)}\right)\right)} = {\color{red}\left(2 \frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)}$$正弦関数の導関数は$$$\frac{d}{dt} \left(\sin{\left(t \right)}\right) = \cos{\left(t \right)}$$$:
$$2 {\color{red}\left(\frac{d}{dt} \left(\sin{\left(t \right)}\right)\right)} = 2 {\color{red}\left(\cos{\left(t \right)}\right)}$$したがって、$$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right) = 2 \cos{\left(t \right)}$$$。
解答
$$$\frac{d}{dt} \left(2 \sin{\left(t \right)}\right) = 2 \cos{\left(t \right)}$$$A
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