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

解

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

6 y^{2} sin (3 x y^{2} - y) cos (3 x y^{2} - y)

解答ステップ

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

y

を定数として扱う

連鎖法則を適用:

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

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

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

= 2 sin (3 x y^{2} - y) cos (3 x y^{2} - y) \cdot 3 y^{2}

簡素化

= 6 y^{2} sin (3 x y^{2} - y) cos (3 x y^{2} - y)