展开 (sin(x)+xcos(x))(3cos(xsin(x)))

解答

展开

(sin (x) + x cos (x)) (3 cos (x sin (x)))

3 cos (x sin (x)) sin (x) + 3 x cos (x sin (x)) cos (x)

求解步骤

(sin (x) + x cos (x)) (3 cos (x sin (x)))

= (3 cos (x sin (x))) (sin (x) + x cos (x))

使用分配律:

a (b + c) = ab + a c

(3 cos (x sin (x))) (sin (x) + x cos (x)) = 3 cos (x sin (x)) sin (x) + 3 cos (x sin (x)) x cos (x)

= 3 cos (x sin (x)) sin (x) + 3 cos (x sin (x)) x cos (x)

= 3 cos (x sin (x)) sin (x) + 3 x cos (x sin (x)) cos (x)

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

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

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

e x p an d A (1, - 4) y B (6, 13)

e x p an d \frac{2 ( e ^{- \frac{3 t}{2}} - 1 )}{3 e ^{- \frac{t}{2}}}