展开 x^2(2cos(x)-4xsin(x)-x^2cos(x))

解答

展开

x^{2} (2 cos (x) - 4 x sin (x) - x^{2} cos (x))

2 x^{2} cos (x) - 4 x^{3} sin (x) - x^{4} cos (x)

求解步骤

x^{2} (2 cos (x) - 4 x sin (x) - x^{2} cos (x))

使用分配律:

m (a + b + c) = ma + mb + m c

x^{2} (2 cos (x) - 4 x sin (x) - x^{2} cos (x)) = x^{2} \cdot 2 cos (x) + x^{2} (- 4 x sin (x)) + x^{2} (- x^{2} cos (x))

= x^{2} \cdot 2 cos (x) + x^{2} (- 4 x sin (x)) + x^{2} (- x^{2} cos (x))

化简

x^{2} \cdot 2 cos (x) + x^{2} (- 4 x sin (x)) + x^{2} (- x^{2} cos (x)) : 2 x^{2} cos (x) - 4 x^{3} sin (x) - x^{4} cos (x)

= 2 x^{2} cos (x) - 4 x^{3} sin (x) - x^{4} cos (x)

e x p an d (5 - 5 \frac{x}{244140625})^{19}

e x p an d (x + e^{x})^{2}

e x p an d e^{3 x} (4 - 2 x) - 2

e x p an d - \frac{3}{16} (- \frac{19}{4} + (- \frac{3}{4} ln (\frac{9}{57 - 64 x})))

e x p an d (2 sin (2 t)) (1 + 2 sin^{2} (t))