展开 x(dvx+vdx)

解答

展开

x (d vx + v d x)

x^{2} d v + xv d x

求解步骤

x (d vx + v d x)

= x (x d v + v d x)

使用分配律:

a (b + c) = ab + a c

a = x, b = d vx, c = v d x

= x d vx + xv d x

= xx d v + xv d x

xx d v = x^{2} d v

= x^{2} d v + xv d x

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

e x p an d \frac{3 x - 7 x}{8 x ^{2}} + \frac{6 x ^{2} + 2 x}{8 x ^{2}}

e x p an d 2 (4 ln (2) + 4)

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

e x p an d lo g_{10} (\frac{2 x}{y})