(\partial)/(\partial y)(cos(xy)x)

解

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

- x^{2} sin (x y)

解答ステップ

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

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) = x

= x (- sin (x y) x)

簡素化

x (- sin (x y) x) : - x^{2} sin (x y)

= - x^{2} sin (x y)