cot(az)の微分

\(cot\left(az\right)\)の微分

\begin{eqnarray} \frac{\mathrm{d}}{\mathrm{d}z}\cot{\left(az\right)} &=&\frac{\mathrm{d}}{\mathrm{d}w}\cot{\left(w\right)}\frac{\mathrm{d}w}{\mathrm{d}z} \\&&\;\ldots\;a\in\mathbb{R},\;z\in\mathbb{C} \\&&\;\ldots\;\href{https://shikitenkai.blogspot.com/2021/07/wz.html}{w=az,\;\frac{\mathrm{d}w}{\mathrm{d}z}=a} \\&=&\frac{-1}{\sin^2{\left(az\right)}}\cdot a \;\ldots\;\href{https://shikitenkai.blogspot.com/2021/07/cotz.html}{\frac{\mathrm{d}}{\mathrm{d}w}\cot{\left(w\right)}=\frac{-1}{\sin^2{\left(w\right)}}} \\&=&-\frac{a}{\sin^2{\left(az\right)}} \end{eqnarray}