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$$$\frac{\cos{\left(t \right)}}{3}$$$の導関数
入力内容
$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)$$$ 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 $$$c = \frac{1}{3}$$$ と $$$f{\left(t \right)} = \cos{\left(t \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dt} \left(\cos{\left(t \right)}\right)}{3}\right)}$$余弦関数の導関数は$$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:
$$\frac{{\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)}}{3} = \frac{{\color{red}\left(- \sin{\left(t \right)}\right)}}{3}$$したがって、$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$。
解答
$$$\frac{d}{dt} \left(\frac{\cos{\left(t \right)}}{3}\right) = - \frac{\sin{\left(t \right)}}{3}$$$A
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