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

解

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

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

解答ステップ

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

x

を定数として扱う

連鎖法則を適用:

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

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

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

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

簡素化

= 4 y cos (3 x - y^{2}) sin (3 x - y^{2})