erweitern (4x+5)(xln(x)-x)

Lösung

erweitern

(4 x + 5) (x ln (x) - x)

4 x^{2} ln (x) - 4 x^{2} + 5 x ln (x) - 5 x

Schritte zur Lösung

(4 x + 5) (x ln (x) - x)

Wende Ausklammerungsregel an (VANI):

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

a = 4 x, b = 5, c = x ln (x), d = - x

= 4 xx ln (x) + 4 x (- x) + 5 x ln (x) + 5 (- x)

Wende Minus-Plus Regeln an

+ (- a) = - a

= 4 xx ln (x) - 4 xx + 5 x ln (x) - 5 x

Vereinfache

4 xx ln (x) - 4 xx + 5 x ln (x) - 5 x : 4 x^{2} ln (x) - 4 x^{2} + 5 x ln (x) - 5 x

= 4 x^{2} ln (x) - 4 x^{2} + 5 x ln (x) - 5 x

e x p an d e^{t - 2} U (t - 2)

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

e x p an d 2 e^{- x} x - e^{- x} (x^{2} - 1)

e x p an d y^{''} (x) - 4 x y^{'} (x) + (4 x^{2} - 2) y

\frac{d ^{3}}{d x ^{3}} ((y) (2 x^{2} - \frac{1}{x ^{3}}))