erweitern ((e^x-1)(e^{2y}-1))/(xy)

Lösung

erweitern

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

\frac{e ^{x + 2 y}}{x y} - \frac{e ^{x}}{x y} - \frac{e ^{2 y}}{x y} + \frac{1}{x y}

Schritte zur Lösung

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

Multipliziere aus

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

= \frac{e ^{x + 2 y} - e ^{x} - e ^{2 y} + 1}{x y}

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{e ^{x + 2 y} - e ^{x} - e ^{2 y} + 1}{x y} = \frac{e ^{x + 2 y}}{x y} - \frac{e ^{x}}{x y} - \frac{e ^{2 y}}{x y} + \frac{1}{x y}

= \frac{e ^{x + 2 y}}{x y} - \frac{e ^{x}}{x y} - \frac{e ^{2 y}}{x y} + \frac{1}{x y}

e x p an d \frac{15 ( s + 20 )}{15 s ^{3} + s + 1}

e x p an d x (x - 1) y^{''} (x) + 6 x^{2} y^{'} (x) + 3 y

e x p an d (315 + 5) x

e x p an d \frac{3 ( 2 \cdot 4 ^{\frac{1}{3}} - 2 ^{\frac{1}{3}} )}{2}

e x p an d (t + 1) \cdot \frac{df}{d t}