erweitern (e^{x^2}-e^{-x^2})^2

Lösung

erweitern

(e^{x^{2}} - e^{- x^{2}})^{2}

e^{2 x^{2}} - 2 + e^{- 2 x^{2}}

Schritte zur Lösung

(e^{x^{2}} - e^{- x^{2}})^{2}

Wende Formel für perfekte quadratische Gleichungen an:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = e^{x^{2}}, b = e^{- x^{2}}

= (e^{x^{2}})^{2} - 2 e^{x^{2}} e^{- x^{2}} + (e^{- x^{2}})^{2}

Vereinfache

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

= e^{2 x^{2}} - 2 + e^{- 2 x^{2}}

s im pl i f y (4 + 3 i)^{6}

e x p an d (28500 + 1000 ln (\frac{33}{14})) (\frac{1}{57})

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} - 1)^{3})

e x p an d (e^{2 x}) (\frac{x}{4} + A) + (e^{- 2 x}) (\frac{1}{16} e^{4 x} + B)

\frac{d ^{2}}{d x ^{2}} ((y) ((a \cdot x) + ((1 - a) \cdot x^{2})))