(\partial)/(\partial y)(arctan(x-y))

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

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