$$$\frac{\cosh{\left(v \right)}}{5}$$$の導関数
入力内容
$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right)$$$ を求めよ。
解答
定数倍の法則 $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$ を $$$c = \frac{1}{5}$$$ と $$$f{\left(v \right)} = \cosh{\left(v \right)}$$$ に対して適用します:
$${\color{red}\left(\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dv} \left(\cosh{\left(v \right)}\right)}{5}\right)}$$双曲線余弦の導関数は$$$\frac{d}{dv} \left(\cosh{\left(v \right)}\right) = \sinh{\left(v \right)}$$$です:
$$\frac{{\color{red}\left(\frac{d}{dv} \left(\cosh{\left(v \right)}\right)\right)}}{5} = \frac{{\color{red}\left(\sinh{\left(v \right)}\right)}}{5}$$したがって、$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right) = \frac{\sinh{\left(v \right)}}{5}$$$。
解答
$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right) = \frac{\sinh{\left(v \right)}}{5}$$$A