erweitern rx(rx-1)ke^{rx-2}

Lösung

erweitern

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

k e^{r x - 2} r^{2} x^{2} - k e^{r x - 2} r x

Schritte zur Lösung

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

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

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = r x k e^{r x - 2}, b = r x, c = 1

= r x k e^{r x - 2} r x - r x k e^{r x - 2} \cdot 1

= k e^{r x - 2} rr xx - 1 \cdot k e^{r x - 2} r x

Vereinfache

k e^{r x - 2} rr xx - 1 \cdot k e^{r x - 2} r x : k e^{r x - 2} r^{2} x^{2} - k e^{r x - 2} r x

= k e^{r x - 2} r^{2} x^{2} - k e^{r x - 2} r x

e x p an d (x^{3} + 7) e^{2}

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

e x p an d 3 (x + Δ x)^{4} + (2 (x + Δ x) - 1)^{2}

e x p an d \frac{2 g ( h - g )}{g h - j}

e x p an d - 20 (8 e - 20)