(\partial)/(\partial x)(ln(((x+y))/(x-y)))

解

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

- \frac{2 y}{( x + y ) ( x - y )}

解答ステップ

\frac{\partial}{\partial x} (ln (\frac{( x + y )}{x - y}))

y

を定数として扱う

連鎖法則を適用:

\frac{1}{\frac{x + y}{x - y}} \frac{\partial}{\partial x} (\frac{x + y}{x - y})

= \frac{1}{\frac{x + y}{x - y}} \frac{\partial}{\partial x} (\frac{x + y}{x - y})

\frac{\partial}{\partial x} (\frac{x + y}{x - y}) = - \frac{2 y}{( x - y ) ^{2}}

= \frac{1}{\frac{x + y}{x - y}} (- \frac{2 y}{( x - y ) ^{2}})

簡素化

\frac{1}{\frac{x + y}{x - y}} (- \frac{2 y}{( x - y ) ^{2}}) : - \frac{2 y}{( x + y ) ( x - y )}

= - \frac{2 y}{( x + y ) ( x - y )}