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$$$\frac{\sin{\left(u \right)}}{2}$$$の導関数
入力内容
$$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{2}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{du} \left(c f{\left(u \right)}\right) = c \frac{d}{du} \left(f{\left(u \right)}\right)$$$ を $$$c = \frac{1}{2}$$$ と $$$f{\left(u \right)} = \sin{\left(u \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{2}\right)\right)} = {\color{red}\left(\frac{\frac{d}{du} \left(\sin{\left(u \right)}\right)}{2}\right)}$$正弦関数の導関数は$$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\frac{{\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{2} = \frac{{\color{red}\left(\cos{\left(u \right)}\right)}}{2}$$したがって、$$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{2}\right) = \frac{\cos{\left(u \right)}}{2}$$$。
解答
$$$\frac{d}{du} \left(\frac{\sin{\left(u \right)}}{2}\right) = \frac{\cos{\left(u \right)}}{2}$$$A
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