$$$\frac{\sqrt{7} \sin{\left(u \right)}}{7}$$$の導関数
関連する計算機: 対数微分計算機, 陰関数微分計算機（手順付き）
入力内容
$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)$$$ 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 $$$c = \frac{\sqrt{7}}{7}$$$ と $$$f{\left(u \right)} = \sin{\left(u \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right)\right)} = {\color{red}\left(\frac{\sqrt{7}}{7} \frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}$$正弦関数の導関数は$$$\frac{d}{du} \left(\sin{\left(u \right)}\right) = \cos{\left(u \right)}$$$:
$$\frac{\sqrt{7} {\color{red}\left(\frac{d}{du} \left(\sin{\left(u \right)}\right)\right)}}{7} = \frac{\sqrt{7} {\color{red}\left(\cos{\left(u \right)}\right)}}{7}$$したがって、$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$。
解答
$$$\frac{d}{du} \left(\frac{\sqrt{7} \sin{\left(u \right)}}{7}\right) = \frac{\sqrt{7} \cos{\left(u \right)}}{7}$$$A