展开 (derivative of 3)/(2(2x^4+5x^2+3)^4)

解答

展开

\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}

求解步骤

\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 )}

乘开

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}

e x p an d \frac{3}{4} (3 - \frac{x}{9}) - \frac{1}{6} (1 - \frac{x}{3} = 1 - (x - \frac{3}{2}))

s im pl i f y (2 + 3 x i)^{2}

e x p an d \frac{5 x + 31}{( x + 2 ) ( x + 5 )}

s im pl i f y (\frac{x}{2} - 1) (x - 3)

s im pl i f y (1 - 4 x)^{2}