(\partial)/(\partial x)(2xy+5y^2-3xy^3)

解

\frac{\partial}{\partial x} (2 x y + 5 y^{2} - 3 x y^{3})

- 3 y^{3} + 2 y

解答ステップ

\frac{\partial}{\partial x} (2 x y + 5 y^{2} - 3 x y^{3})

y

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 x} (2 x y) + \frac{\partial}{\partial x} (5 y^{2}) - \frac{\partial}{\partial x} (3 x y^{3})

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

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

= 2 y + 0 - 3 y^{3}

簡素化

= - 3 y^{3} + 2 y