展開する (\partial)/(\partial x)(6(2x+y)^2*(x-2y))+(2x+y)^3

解

展開する

\frac{\partial}{\partial x} (6 (2 x + y)^{2} \cdot (x - 2 y)) + (2 x + y)^{3}

\frac{\partial}{\partial x} (24 x^{3} - 24 x^{2} y - 42 x y^{2} - 12 y^{3}) + 8 x^{3} + 12 x^{2} y + 6 x y^{2} + y^{3}

解答ステップ

\frac{\partial}{\partial x} (6 (2 x + y)^{2} (x - 2 y)) + (2 x + y)^{3}

\frac{\partial}{\partial x} (6 (2 x + y)^{2} (x - 2 y)) = \frac{\partial}{\partial x} (24 x^{3} - 24 x^{2} y - 42 x y^{2} - 12 y^{3})

= \frac{\partial}{\partial x} (24 x^{3} - 24 x^{2} y - 42 x y^{2} - 12 y^{3}) + (2 x + y)^{3}

(2 x + y)^{3} : 8 x^{3} + 12 x^{2} y + 6 x y^{2} + y^{3}

= \frac{\partial}{\partial x} (24 x^{3} - 24 x^{2} y - 42 x y^{2} - 12 y^{3}) + 8 x^{3} + 12 x^{2} y + 6 x y^{2} + y^{3}