vereinfachen e^{-2/5 x}(-2/5 xe^{-2/5 x}+e^{-2/5 x})

Lösung

vereinfachen

e^{- \frac{2}{5} x} (- \frac{2}{5} x e^{- \frac{2}{5} x} + e^{- \frac{2}{5} x})

\frac{- 2 x + 5}{5 e ^{\frac{4 x}{5}}}

Schritte zur Lösung

e^{- \frac{2}{5} x} (- \frac{2}{5} x e^{- \frac{2}{5} x} + e^{- \frac{2}{5} x})

Wende Exponentenregel an:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{\frac{2}{5} x}} (- \frac{2}{5} e^{- \frac{2}{5} x} x + e^{- \frac{2}{5} x})

\frac{1}{e ^{\frac{2}{5} x}} = \frac{1}{e ^{\frac{2 x}{5}}}

= \frac{1}{e ^{\frac{2 x}{5}}} (- \frac{2}{5} e^{- \frac{2}{5} x} x + e^{- \frac{2}{5} x})

\frac{2}{5} x e^{- \frac{2}{5} x} = \frac{2 e ^{- \frac{2 x}{5}} x}{5}

e^{- \frac{2}{5} x} = e^{- \frac{2 x}{5}}

= \frac{1}{e ^{\frac{2 x}{5}}} (- \frac{2 e ^{- \frac{2 x}{5}} x}{5} + e^{- \frac{2 x}{5}})

Multipliziere Brüche:

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

= \frac{1 \cdot ( - \frac{2 x e ^{- \frac{2 x}{5}}}{5} + e ^{- \frac{2 x}{5}} )}{e ^{\frac{2 x}{5}}}

1 \cdot (- \frac{2 x e ^{- \frac{2 x}{5}}}{5} + e^{- \frac{2 x}{5}}) = - \frac{2 e ^{- \frac{2 x}{5}} x}{5} + e^{- \frac{2 x}{5}}

= \frac{- \frac{2 e ^{- \frac{2 x}{5}} x}{5} + e ^{- \frac{2 x}{5}}}{e ^{\frac{2 x}{5}}}

Füge

- \frac{2 x e ^{- \frac{2 x}{5}}}{5} + e^{- \frac{2 x}{5}}

zusammen:

\frac{- 2 x + 5}{5 e ^{\frac{2 x}{5}}}

= \frac{\frac{- 2 x + 5}{5 e ^{\frac{2 x}{5}}}}{e ^{\frac{2 x}{5}}}

Wende Bruchregel an:

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

= \frac{- 2 x + 5}{e ^{\frac{2 x}{5}} \cdot 5 e ^{\frac{2 x}{5}}}

e^{\frac{2 x}{5}} \cdot 5 e^{\frac{2 x}{5}} = 5 e^{2 \cdot \frac{2 x}{5}}

= \frac{- 2 x + 5}{5 e ^{2 \cdot \frac{2 x}{5}}}

e^{2 \cdot \frac{2 x}{5}} = e^{\frac{4 x}{5}}

= \frac{- 2 x + 5}{5 e ^{\frac{4 x}{5}}}

s im pl i f y (sin^{2} (x))^{\frac{3}{2}}

s im pl i f y (400 \cdot 1 0^{- 3}) (0.6 \cdot 1 0^{6})^{2}

s im pl i f y e^{- 0.0752} [0.5 \cdot 0.6315]

s im pl i f y (7.72 \cdot 1 0^{- 2}) (3.17)

\frac{d}{d x} ((t) e^{- t})