$$$\cos{\left(t \right)} + 1$$$の導関数
入力内容
$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)$$$ を求めよ。
解答
和/差の導関数は、導関数の和/差である:
$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right)\right)} = {\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right) + \frac{d}{dt} \left(1\right)\right)}$$定数の導数は$$$0$$$です:
$${\color{red}\left(\frac{d}{dt} \left(1\right)\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right) = {\color{red}\left(0\right)} + \frac{d}{dt} \left(\cos{\left(t \right)}\right)$$余弦関数の導関数は$$$\frac{d}{dt} \left(\cos{\left(t \right)}\right) = - \sin{\left(t \right)}$$$:
$${\color{red}\left(\frac{d}{dt} \left(\cos{\left(t \right)}\right)\right)} = {\color{red}\left(- \sin{\left(t \right)}\right)}$$したがって、$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$。
解答
$$$\frac{d}{dt} \left(\cos{\left(t \right)} + 1\right) = - \sin{\left(t \right)}$$$A
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