(\partial)/(\partial x)(-2kl(ln(y/(-x-y))))

解

\frac{\partial}{\partial x} (- 2 k l (ln (\frac{y}{- x - y})))

- \frac{2 l k}{- x - y}

解答ステップ

\frac{\partial}{\partial x} (- 2 k l (ln (\frac{y}{- x - y})))

l, k, y

を定数として扱う

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 k l \frac{\partial}{\partial x} (ln (\frac{y}{- x - y}))

連鎖法則を適用:

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

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

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

= - 2 k l \frac{1}{\frac{y}{- x - y}} \cdot \frac{y}{( - x - y ) ^{2}}

簡素化

- 2 k l \frac{1}{\frac{y}{- x - y}} \cdot \frac{y}{( - x - y ) ^{2}} : - \frac{2 l k}{- x - y}

= - \frac{2 l k}{- x - y}