展開する (derivative of 3)/(2(2x^4+5x^2+3)^4)

解

展開する

\frac{\frac{d}{d x} ( 3 )}{2 ( 2 x ^{4} + 5 x ^{2} + 3 ) ^{4}}

\frac{\frac{d}{d x} ( 3 )}{32 x ^{16} + 320 x ^{14} + 1392 x ^{12} + 3440 x ^{10} + 5282 x ^{8} + 5160 x ^{6} + 3132 x ^{4} + 1080 x ^{2} + 162}

解答ステップ

\frac{\frac{d}{d x} ( 3 )}{2 ( 2 x ^{4} + 5 x ^{2} + 3 ) ^{4}}

(2 x^{4} + 5 x^{2} + 3)^{4} = 16 x^{16} + 160 x^{14} + 696 x^{12} + 1720 x^{10} + 2641 x^{8} + 2580 x^{6} + 1566 x^{4} + 540 x^{2} + 81

= \frac{\frac{d}{d x} ( 3 )}{2 ( 16 x ^{16} + 160 x ^{14} + 696 x ^{12} + 1720 x ^{10} + 2641 x ^{8} + 2580 x ^{6} + 1566 x ^{4} + 540 x ^{2} + 81 )}

拡張

2 (16 x^{16} + 160 x^{14} + 696 x^{12} + 1720 x^{10} + 2641 x^{8} + 2580 x^{6} + 1566 x^{4} + 540 x^{2} + 81) : 32 x^{16} + 320 x^{14} + 1392 x^{12} + 3440 x^{10} + 5282 x^{8} + 5160 x^{6} + 3132 x^{4} + 1080 x^{2} + 162

= \frac{\frac{d}{d x} ( 3 )}{32 x ^{16} + 320 x ^{14} + 1392 x ^{12} + 3440 x ^{10} + 5282 x ^{8} + 5160 x ^{6} + 3132 x ^{4} + 1080 x ^{2} + 162}