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

解

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

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

解答ステップ

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

y

を定数として扱う

定数を除去:

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

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

連鎖法則を適用:

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

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

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

= - y^{2} cos (x y^{2}) y^{2}

簡素化

- y^{2} cos (x y^{2}) y^{2} : - y^{4} cos (y^{2} x)

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