(\partial)/(\partial y)(2x^3-11x^2y+3y^2)

解

\frac{\partial}{\partial y} (2 x^{3} - 11 x^{2} y + 3 y^{2})

6 y - 11 x^{2}

解答ステップ

\frac{\partial}{\partial y} (2 x^{3} - 11 x^{2} y + 3 y^{2})

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 x^{3}) - \frac{\partial}{\partial y} (11 x^{2} y) + \frac{\partial}{\partial y} (3 y^{2})

\frac{\partial}{\partial y} (2 x^{3}) = 0

\frac{\partial}{\partial y} (11 x^{2} y) = 11 x^{2}

\frac{\partial}{\partial y} (3 y^{2}) = 6 y

= 0 - 11 x^{2} + 6 y

簡素化

= 6 y - 11 x^{2}