erweitern (sqrt(x))e^{x^2}(x^2+7)^{10}

Lösung

erweitern

(x) e^{x^{2}} (x^{2} + 7)^{10}

e^{x^{2}} x^{20} x + 70 e^{x^{2}} x^{18} x + 2205 e^{x^{2}} x^{16} x + 41160 e^{x^{2}} x^{14} x + 504210 e^{x^{2}} x^{12} x + 4235364 e^{x^{2}} x^{10} x + 24706290 e^{x^{2}} x^{8} x + 98825160 e^{x^{2}} x^{6} x + 259416045 e^{x^{2}} x^{4} x + 403536070 e^{x^{2}} x^{2} x + 282475249 e^{x^{2}} x

Schritte zur Lösung

(x) e^{x^{2}} (x^{2} + 7)^{10}

Entferne die Klammern:

(a) = a

= x e^{x^{2}} (x^{2} + 7)^{10}

(x^{2} + 7)^{10} = x^{20} + 70 x^{18} + 2205 x^{16} + 41160 x^{14} + 504210 x^{12} + 4235364 x^{10} + 24706290 x^{8} + 98825160 x^{6} + 259416045 x^{4} + 403536070 x^{2} + 282475249

= e^{x^{2}} x (x^{20} + 70 x^{18} + 2205 x^{16} + 41160 x^{14} + 504210 x^{12} + 4235364 x^{10} + 24706290 x^{8} + 98825160 x^{6} + 259416045 x^{4} + 403536070 x^{2} + 282475249)

= e^{x^{2}} x (x^{20} + 70 x^{18} + 2205 x^{16} + 41160 x^{14} + 504210 x^{12} + 4235364 x^{10} + 24706290 x^{8} + 98825160 x^{6} + 259416045 x^{4} + 403536070 x^{2} + 282475249)

Setze Klammern

= x e^{x^{2}} x^{20} + x e^{x^{2}} \cdot 70 x^{18} + x e^{x^{2}} \cdot 2205 x^{16} + x e^{x^{2}} \cdot 41160 x^{14} + x e^{x^{2}} \cdot 504210 x^{12} + x e^{x^{2}} \cdot 4235364 x^{10} + x e^{x^{2}} \cdot 24706290 x^{8} + x e^{x^{2}} \cdot 98825160 x^{6} + x e^{x^{2}} \cdot 259416045 x^{4} + x e^{x^{2}} \cdot 403536070 x^{2} + x e^{x^{2}} \cdot 282475249

= e^{x^{2}} x^{20} x + 70 e^{x^{2}} x^{18} x + 2205 e^{x^{2}} x^{16} x + 41160 e^{x^{2}} x^{14} x + 504210 e^{x^{2}} x^{12} x + 4235364 e^{x^{2}} x^{10} x + 24706290 e^{x^{2}} x^{8} x + 98825160 e^{x^{2}} x^{6} x + 259416045 e^{x^{2}} x^{4} x + 403536070 e^{x^{2}} x^{2} x + 282475249 e^{x^{2}} x

e x p an d \frac{5 ( 131 + 14521 )}{22}

e x p an d 6 (8 - 10 ln (3))

e x p an d \frac{16 V}{s ( s ^{2} + 10 s + 16 )}

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

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