(\partial)/(\partial y)(xcos(x+y))

解

\frac{\partial}{\partial y} (x cos (x + y))

- x sin (x + y)

解答ステップ

\frac{\partial}{\partial y} (x cos (x + y))

x

を定数として扱う

定数を除去:

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

= x \frac{\partial}{\partial y} (cos (x + y))

連鎖法則を適用:

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

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

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

= x (- sin (x + y) \cdot 1)

簡素化

= - x sin (x + y)