erweitern (x-1)e^{(x-1)^2}

Lösung

erweitern

(x - 1) e^{(x - 1)^{2}}

e^{x^{2} - 2 x + 1} x - e^{x^{2} - 2 x + 1}

Schritte zur Lösung

(x - 1) e^{(x - 1)^{2}}

= e^{(x - 1)^{2}} (x - 1)

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = e^{(x - 1)^{2}}, b = x, c = 1

= e^{(x - 1)^{2}} x - e^{(x - 1)^{2}} \cdot 1

= e^{(x - 1)^{2}} x - 1 \cdot e^{(x - 1)^{2}}

Vereinfache

e^{(x - 1)^{2}} x - 1 \cdot e^{(x - 1)^{2}} : e^{x^{2} - 2 x + 1} x - e^{x^{2} - 2 x + 1}

= e^{x^{2} - 2 x + 1} x - e^{x^{2} - 2 x + 1}

e x p an d \frac{( 4 - x ) ( 16 + 5 x ^{2} )}{8}

e x p an d 3 + 3 \frac{3}{4}

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

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

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