(\partial)/(\partial y)(nsin(2(mx+ny)))

解

\frac{\partial}{\partial y} (n sin (2 (m x + n y)))

2 n^{2} cos (2 (m x + n y))

解答ステップ

\frac{\partial}{\partial y} (n sin (2 (m x + n y)))

n, m, x

を定数として扱う

定数を除去:

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

= n \frac{\partial}{\partial y} (sin (2 (m x + n y)))

連鎖法則を適用:

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

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

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

= n cos (2 (m x + n y)) \cdot 2 n

簡素化

n cos (2 (m x + n y)) \cdot 2 n : 2 n^{2} cos (2 (m x + n y))

= 2 n^{2} cos (2 (m x + n y))