展开 2(e^xcos(x))(e^xcos(x)-e^xsin(x))

解答

展开

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

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

求解步骤

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

使用分配律:

a (b - c) = ab - a c

a = 2 (e^{x} cos (x)), b = e^{x} cos (x), c = e^{x} sin (x)

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

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

化简

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

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

e x p an d \frac{1}{( x - 4 ) ( x ^{2} + 1 )}

e x p an d (z^{2} + cos (z)) (2 z - sin (z))

e x p an d \frac{7 x}{( x + 6 ) ^{2}}

s im pl i f y 2 (1 + \frac{2 k}{n})

e x p an d (2 y - 3) d y