展開する Dx[(2x-9)^2(x^3+4x-5)^3]

解

展開する

D x [(2 x - 9)^{2} (x^{3} + 4 x - 5)^{3}]

4 D x^{12} - 36 D x^{11} + 129 D x^{10} - 492 D x^{9} + 1704 D x^{8} - 3423 D x^{7} + 8764 D x^{6} - 15684 D x^{5} + 21099 D x^{4} - 30740 D x^{3} + 28800 D x^{2} - 10125 D x

解答ステップ

D x ((2 x - 9)^{2} (x^{3} + 4 x - 5)^{3})

括弧を削除する:

(a) = a

= D x (2 x - 9)^{2} (x^{3} + 4 x - 5)^{3}

(2 x - 9)^{2} = 4 x^{2} - 36 x + 81

= D x (4 x^{2} - 36 x + 81) (x^{3} + 4 x - 5)^{3}

(x^{3} + 4 x - 5)^{3} = x^{9} + 12 x^{7} - 15 x^{6} + 48 x^{5} - 120 x^{4} + 139 x^{3} - 240 x^{2} + 300 x - 125

= D x (4 x^{2} - 36 x + 81) (x^{9} + 12 x^{7} - 15 x^{6} + 48 x^{5} - 120 x^{4} + 139 x^{3} - 240 x^{2} + 300 x - 125)

拡張

(4 x^{2} - 36 x + 81) (x^{9} + 12 x^{7} - 15 x^{6} + 48 x^{5} - 120 x^{4} + 139 x^{3} - 240 x^{2} + 300 x - 125) : 4 x^{11} - 36 x^{10} + 129 x^{9} - 492 x^{8} + 1704 x^{7} - 3423 x^{6} + 8764 x^{5} - 15684 x^{4} + 21099 x^{3} - 30740 x^{2} + 28800 x - 10125

= D x (4 x^{11} - 36 x^{10} + 129 x^{9} - 492 x^{8} + 1704 x^{7} - 3423 x^{6} + 8764 x^{5} - 15684 x^{4} + 21099 x^{3} - 30740 x^{2} + 28800 x - 10125)

拡張

D x (4 x^{11} - 36 x^{10} + 129 x^{9} - 492 x^{8} + 1704 x^{7} - 3423 x^{6} + 8764 x^{5} - 15684 x^{4} + 21099 x^{3} - 30740 x^{2} + 28800 x - 10125) : 4 D x^{12} - 36 D x^{11} + 129 D x^{10} - 492 D x^{9} + 1704 D x^{8} - 3423 D x^{7} + 8764 D x^{6} - 15684 D x^{5} + 21099 D x^{4} - 30740 D x^{3} + 28800 D x^{2} - 10125 D x

= 4 D x^{12} - 36 D x^{11} + 129 D x^{10} - 492 D x^{9} + 1704 D x^{8} - 3423 D x^{7} + 8764 D x^{6} - 15684 D x^{5} + 21099 D x^{4} - 30740 D x^{3} + 28800 D x^{2} - 10125 D x