展开 (cos(3x+1)sec(2x+1))(12x(2x^3+1)^2)

解答

展开

(cos (3 x + 1) sec (2 x + 1)) (12 x (2 x^{3} + 1)^{2})

48 x^{7} cos (3 x + 1) sec (2 x + 1) + 48 x^{4} cos (3 x + 1) sec (2 x + 1) + 12 x cos (3 x + 1) sec (2 x + 1)

求解步骤

(cos (3 x + 1) sec (2 x + 1)) (12 x (2 x^{3} + 1)^{2})

去除括号:

(a) = a

= cos (3 x + 1) sec (2 x + 1) \cdot 12 x (2 x^{3} + 1)^{2}

(2 x^{3} + 1)^{2} = 4 x^{6} + 4 x^{3} + 1

= 12 x cos (3 x + 1) sec (2 x + 1) (4 x^{6} + 4 x^{3} + 1)

= 12 x cos (3 x + 1) sec (2 x + 1) (4 x^{6} + 4 x^{3} + 1)

打开括号

= cos (3 x + 1) sec (2 x + 1) \cdot 12 x \cdot 4 x^{6} + cos (3 x + 1) sec (2 x + 1) \cdot 12 x \cdot 4 x^{3} + cos (3 x + 1) sec (2 x + 1) \cdot 12 x \cdot 1

= 12 \cdot 4 x^{6} x cos (3 x + 1) sec (2 x + 1) + 12 \cdot 4 x^{3} x cos (3 x + 1) sec (2 x + 1) + 12 \cdot 1 \cdot x cos (3 x + 1) sec (2 x + 1)

化简

12 \cdot 4 x^{6} x cos (3 x + 1) sec (2 x + 1) + 12 \cdot 4 x^{3} x cos (3 x + 1) sec (2 x + 1) + 12 \cdot 1 \cdot x cos (3 x + 1) sec (2 x + 1) : 48 x^{7} cos (3 x + 1) sec (2 x + 1) + 48 x^{4} cos (3 x + 1) sec (2 x + 1) + 12 x cos (3 x + 1) sec (2 x + 1)

= 48 x^{7} cos (3 x + 1) sec (2 x + 1) + 48 x^{4} cos (3 x + 1) sec (2 x + 1) + 12 x cos (3 x + 1) sec (2 x + 1)

e x p an d 7^{2} \cdot 3

\frac{d ^{2}}{d x ^{2}} ((x) (5 x cos (3 x) + 8 x sin (3 x)))

e x p an d sin (k (t - k u))

e x p an d 6.7 x + 2.8 x

e x p an d 2 \cdot \frac{1 0 ^{2} \cdot 3 \cdot 2 ^{4}}{2 - 3} - (5^{2} \cdot 2 - 7 \cdot 3)