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

解

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

- 2 cos (y) + 3 x y^{2}

解答ステップ

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

x

を定数として扱う

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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