(\partial)/(\partial x)(sin^2(x-5y))

解

\frac{\partial}{\partial x} (sin^{2} (x - 5 y))

sin (2 (x - 5 y))

解答ステップ

\frac{\partial}{\partial x} (sin^{2} (x - 5 y))

y

を定数として扱う

連鎖法則を適用:

2 sin (x - 5 y) \frac{\partial}{\partial x} (sin (x - 5 y))

= 2 sin (x - 5 y) \frac{\partial}{\partial x} (sin (x - 5 y))

\frac{\partial}{\partial x} (sin (x - 5 y)) = cos (x - 5 y)

= 2 sin (x - 5 y) cos (x - 5 y)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

= sin (2 (x - 5 y))