展开 e^xsin(x)(e^xcos(x)-e^xsin(x))

解答

展开

e^{x} sin (x) (e^{x} cos (x) - e^{x} sin (x))

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

求解步骤

e^{x} sin (x) (e^{x} cos (x) - e^{x} sin (x))

使用分配律:

a (b - c) = ab - a c

a = e^{x} sin (x), b = e^{x} cos (x), c = e^{x} sin (x)

= e^{x} sin (x) e^{x} cos (x) - e^{x} sin (x) e^{x} sin (x)

= e^{x} e^{x} sin (x) cos (x) - e^{x} e^{x} sin (x) sin (x)

化简

e^{x} e^{x} sin (x) cos (x) - e^{x} e^{x} sin (x) sin (x) : e^{2 x} sin (x) cos (x) - e^{2 x} sin^{2} (x)

= e^{2 x} sin (x) cos (x) - e^{2 x} sin^{2} (x)

e x p an d (D + 1) (D + x) e^{x}

s im pl i f y 4 (sin (2 x) - cos (2 x))

s im pl i f y (3 + 4 i)^{5}

e x p an d 9 (\frac{3}{5} x + \frac{4}{5} y)^{2}

e x p an d (a - 1 + x) l e f t (a - 1 - x)