展开 1/((x^3-2x^2+7)^4)

解答

展开

\frac{1}{( x ^{3} - 2 x ^{2} + 7 ) ^{4}}

\frac{1}{x ^{12} - 8 x ^{11} + 24 x ^{10} - 4 x ^{9} - 152 x ^{8} + 336 x ^{7} + 70 x ^{6} - 1176 x ^{5} + 1176 x ^{4} + 1372 x ^{3} - 2744 x ^{2} + 2401}

求解步骤

\frac{1}{( x ^{3} - 2 x ^{2} + 7 ) ^{4}}

(x^{3} - 2 x^{2} + 7)^{4} = x^{12} - 8 x^{11} + 24 x^{10} - 4 x^{9} - 152 x^{8} + 336 x^{7} + 70 x^{6} - 1176 x^{5} + 1176 x^{4} + 1372 x^{3} - 2744 x^{2} + 2401

= \frac{1}{x ^{12} - 8 x ^{11} + 24 x ^{10} - 4 x ^{9} - 152 x ^{8} + 336 x ^{7} + 70 x ^{6} - 1176 x ^{5} + 1176 x ^{4} + 1372 x ^{3} - 2744 x ^{2} + 2401}

e x p an d 2 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

e x p an d y^{'} (x) 3 x^{2} + 3 y^{2} (y^{'} (x)) - 5.4 (y + x (y^{'} (x)))

e x p an d 4 x - 4 x H (x - 5) + 20 (H - 5)

e x p an d \frac{d}{d x} ((x^{3} + 1) e^{x}) - 15 \cdot arcsinh (x)

e x p an d (1 + sin (θ))^{3}