展開する 3(6x+9y)^2(6+9y'(x))

解

展開する

3 (6 x + 9 y)^{2} (6 + 9 y^{'} (x))

648 x^{2} + 1944 x y + 1458 y^{2} + 972 x^{2} y' (x) + 2916 x y' (x) y + 2187 y' (x) y^{2}

解答ステップ

3 (6 x + 9 y)^{2} (6 + 9 y^{'} (x))

分配法則を適用する:

a (b + c) = ab + a c

a = 3 (6 x + 9 y)^{2}, b = 6, c = 9 y^{'} (x)

= 3 (6 x + 9 y)^{2} \cdot 6 + 3 (6 x + 9 y)^{2} \cdot 9 y^{^{'}} (x)

= 3 \cdot 6 (6 x + 9 y)^{2} + 3 \cdot 9 (6 x + 9 y)^{2} y^{^{'}} (x)

簡素化

3 \cdot 6 (6 x + 9 y)^{2} + 3 \cdot 9 (6 x + 9 y)^{2} y^{'} (x) : 648 x^{2} + 1944 x y + 1458 y^{2} + 972 x^{2} y^{'} (x) + 2916 x y^{'} (x) y + 2187 y^{'} (x) y^{2}

= 648 x^{2} + 1944 x y + 1458 y^{2} + 972 x^{2} y^{'} (x) + 2916 x y^{'} (x) y + 2187 y^{'} (x) y^{2}