cosh(v)/5的导数

该计算器将求$$$\frac{\cosh{\left(v \right)}}{5}$$$的导数，并显示步骤。

您的输入

求$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right)$$$。

解答

对 $$$c = \frac{1}{5}$$$ 和 $$$f{\left(v \right)} = \cosh{\left(v \right)}$$$ 应用常数倍法则 $$$\frac{d}{dv} \left(c f{\left(v \right)}\right) = c \frac{d}{dv} \left(f{\left(v \right)}\right)$$$：

$${\color{red}\left(\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right)\right)} = {\color{red}\left(\frac{\frac{d}{dv} \left(\cosh{\left(v \right)}\right)}{5}\right)}$$

双曲余弦函数的导数为$$$\frac{d}{dv} \left(\cosh{\left(v \right)}\right) = \sinh{\left(v \right)}$$$：

$$\frac{{\color{red}\left(\frac{d}{dv} \left(\cosh{\left(v \right)}\right)\right)}}{5} = \frac{{\color{red}\left(\sinh{\left(v \right)}\right)}}{5}$$

因此，$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right) = \frac{\sinh{\left(v \right)}}{5}$$$。

答案

$$$\frac{d}{dv} \left(\frac{\cosh{\left(v \right)}}{5}\right) = \frac{\sinh{\left(v \right)}}{5}$$$A