(\partial)/(\partial y)(sin^2(x-3y))

解

\frac{\partial}{\partial y} (sin^{2} (x - 3 y))

- 6 sin (x - 3 y) cos (x - 3 y)

解答ステップ

\frac{\partial}{\partial y} (sin^{2} (x - 3 y))

x

を定数として扱う

連鎖法則を適用:

2 sin (x - 3 y) \frac{\partial}{\partial y} (sin (x - 3 y))

= 2 sin (x - 3 y) \frac{\partial}{\partial y} (sin (x - 3 y))

\frac{\partial}{\partial y} (sin (x - 3 y)) = - 3 cos (x - 3 y)

= 2 sin (x - 3 y) (- 3 cos (x - 3 y))

簡素化

= - 6 sin (x - 3 y) cos (x - 3 y)