erweitern (-2x(x+1)e^2+3e^{2x}-3)/(2e^2)

Lösung

erweitern

\frac{- 2 x ( x + 1 ) e ^{2} + 3 e ^{2 x} - 3}{2 e ^{2}}

- x^{2} - x + \frac{3 e ^{2 x - 2}}{2} - \frac{3}{2 e ^{2}}

Schritte zur Lösung

\frac{- 2 x ( x + 1 ) e ^{2} + 3 e ^{2 x} - 3}{2 e ^{2}}

Multipliziere aus

- 2 x (x + 1) e^{2} + 3 e^{2 x} - 3 : - 2 e^{2} x^{2} - 2 e^{2} x + 3 e^{2 x} - 3

= \frac{- 2 e ^{2} x ^{2} - 2 e ^{2} x + 3 e ^{2 x} - 3}{2 e ^{2}}

Wende Bruchregel an:

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

\frac{- 2 e ^{2} x ^{2} - 2 e ^{2} x + 3 e ^{2 x} - 3}{2 e ^{2}} = - \frac{2 e ^{2} x ^{2}}{2 e ^{2}} - \frac{2 e ^{2} x}{2 e ^{2}} + \frac{3 e ^{2 x}}{2 e ^{2}} - \frac{3}{2 e ^{2}}

= - \frac{2 e ^{2} x ^{2}}{2 e ^{2}} - \frac{2 e ^{2} x}{2 e ^{2}} + \frac{3 e ^{2 x}}{2 e ^{2}} - \frac{3}{2 e ^{2}}

Streiche

\frac{2 e ^{2} x ^{2}}{2 e ^{2}} : x^{2}

= - x^{2} - \frac{2 e ^{2} x}{2 e ^{2}} + \frac{3 e ^{2 x}}{2 e ^{2}} - \frac{3}{2 e ^{2}}

Streiche

\frac{2 e ^{2} x}{2 e ^{2}} : x

= - x^{2} - x + \frac{3 e ^{2 x}}{2 e ^{2}} - \frac{3}{2 e ^{2}}

Streiche

\frac{3 e ^{2 x}}{2 e ^{2}} : \frac{3 e ^{2 x - 2}}{2}

= - x^{2} - x + \frac{3 e ^{2 x - 2}}{2} - \frac{3}{2 e ^{2}}

\frac{\partial}{\partial x} ((z) (sin (z) - x yz))

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

e x p an d - 3 (5 + 7)

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

\frac{\partial}{\partial x} ((z) (e^{x yz} - x - y))