展开 (u^2y^2-y^2)(udy+ydu)

解答

展开

(u^{2} y^{2} - y^{2}) (u d y + y d u)

u^{3} y^{2} d y + u^{2} y^{3} d u - u y^{2} d y - y^{3} d u

求解步骤

(u^{2} y^{2} - y^{2}) (u d y + y d u)

使用 FOIL 方法:

(a + b) (c + d) = a c + a d + b c + b d

a = u^{2} y^{2}, b = - y^{2}, c = u d y, d = y d u

= u^{2} y^{2} u d y + u^{2} y^{2} y d u + (- y^{2}) u d y + (- y^{2}) y d u

使用加减运算法则

+ (- a) = - a

= u^{2} u y^{2} d y + u^{2} y^{2} y d u - u y^{2} d y - y^{2} y d u

化简

u^{2} u y^{2} d y + u^{2} y^{2} y d u - u y^{2} d y - y^{2} y d u : u^{3} y^{2} d y + u^{2} y^{3} d u - u y^{2} d y - y^{3} d u

= u^{3} y^{2} d y + u^{2} y^{3} d u - u y^{2} d y - y^{3} d u

e x p an d (- 4) (- 3) (2) (- 5)

e x p an d t^{2} \cdot d i r a c (t - π)

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

\frac{d}{d t} ((X) ((X - 1) (1 - 2 X)))

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