erweitern-(-x^2+2x+3}{16e^{\frac{(x-1)^2)/8}}

Lösung

erweitern

- \frac{- x ^{2} + 2 x + 3}{16 e ^{\frac{( x - 1 ) ^{2}}{8}}}

\frac{x ^{2}}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{x}{8 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}

Schritte zur Lösung

- \frac{- x ^{2} + 2 x + 3}{16 e ^{\frac{( x - 1 ) ^{2}}{8}}}

e^{\frac{( x - 1 ) ^{2}}{8}} = e^{\frac{x ^{2} - 2 x + 1}{8}}

= - \frac{- x ^{2} + 2 x + 3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}

Wende Bruchregel an:

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

\frac{- x ^{2} + 2 x + 3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} = - (- \frac{x ^{2}}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}) - (\frac{2 x}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}) - (\frac{3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}})

= - (- \frac{x ^{2}}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}) - (\frac{2 x}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}) - (\frac{3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}})

Entferne die Klammern:

(a) = a, - (- a) = a

= \frac{x ^{2}}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{2 x}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}

Streiche

\frac{2 x}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} : \frac{x}{8 e ^{\frac{x ^{2} - 2 x + 1}{8}}}

= \frac{x ^{2}}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{x}{8 e ^{\frac{x ^{2} - 2 x + 1}{8}}} - \frac{3}{16 e ^{\frac{x ^{2} - 2 x + 1}{8}}}

e x p an d sin (π (t)) - e^{- s} (sin (π (t + 1)))

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