erweitern (3x+vx)(vdx+xdv)

Lösung

erweitern

(3 x + vx) (v d x + x d v)

3 vx d x + 3 x^{2} d v + v^{2} x d x + v x^{2} d v

Schritte zur Lösung

(3 x + vx) (v d x + x d v)

Wende Ausklammerungsregel an (VANI):

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

a = 3 x, b = vx, c = v d x, d = x d v

= 3 xv d x + 3 xx d v + vxv d x + vxx d v

= 3 vx d x + 3 xx d v + vvx d x + vxx d v

Vereinfache

3 vx d x + 3 xx d v + vvx d x + vxx d v : 3 vx d x + 3 x^{2} d v + v^{2} x d x + v x^{2} d v

= 3 vx d x + 3 x^{2} d v + v^{2} x d x + v x^{2} d v

e x p an d \frac{( 4 x + 1 ) ( 5 x - 1 )}{x ^{2} - 4}

e x p an d Q_{0} (1 - e^{- \frac{y}{a}})

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

e x p an d \frac{9 - 4 y}{4}

e x p an d \frac{3 x + 1}{x ( 9 - x )}