(\partial)/(\partial y)((x)(2x+ycos(xy)))

解

\frac{\partial}{\partial y} ((x) (2 x + y cos (x y)))

x (cos (x y) - x y sin (x y))

解答ステップ

\frac{\partial}{\partial y} ((x) (2 x + y 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} (2 x + y cos (x y))

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial y} (2 x) = 0

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

= x (0 + cos (x y) - x y sin (x y))

簡素化

= x (cos (x y) - x y sin (x y))