(\partial)/(\partial y)(2sin(y^2))

解

\frac{\partial}{\partial y} (2 sin (y^{2}))

4 y cos (y^{2})

解答ステップ

\frac{\partial}{\partial y} (2 sin (y^{2}))

定数を除去:

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

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

連鎖法則を適用:

cos (y^{2}) \frac{\partial}{\partial y} (y^{2})

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

\frac{\partial}{\partial y} (y^{2}) = 2 y

= 2 cos (y^{2}) \cdot 2 y

簡素化

= 4 y cos (y^{2})