erweitern 1/3 ((e^{x/3}\H(x))/3+e^{x/3}u'(x)x)

Lösung

erweitern

\frac{1}{3} (\frac{e ^{\frac{x}{3}} H ( x )}{3} + e^{\frac{x}{3}} u^{'} (x) x)

\frac{e ^{\frac{x}{3}} H ( x )}{9} + \frac{e ^{\frac{x}{3}} xu ' ( x )}{3}

Schritte zur Lösung

\frac{1}{3} (\frac{e ^{\frac{x}{3}} H ( x )}{3} + e^{\frac{x}{3}} u^{'} (x) x)

= \frac{1}{3} (\frac{e ^{\frac{x}{3}} H ( x )}{3} + e^{\frac{x}{3}} x u^{^{'}} (x))

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = \frac{1}{3}, b = \frac{e ^{\frac{x}{3}} H ( x )}{3}, c = e^{\frac{x}{3}} u^{'} (x) x

= \frac{1}{3} \cdot \frac{e ^{\frac{x}{3}} H ( x )}{3} + \frac{1}{3} e^{\frac{x}{3}} u^{^{'}} (x) x

= \frac{1}{3} \cdot \frac{e ^{\frac{x}{3}} H ( x )}{3} + \frac{1}{3} e^{\frac{x}{3}} x u^{^{'}} (x)

Vereinfache

\frac{1}{3} \cdot \frac{e ^{\frac{x}{3}} H ( x )}{3} + \frac{1}{3} e^{\frac{x}{3}} x u^{'} (x) : \frac{e ^{\frac{x}{3}} H ( x )}{9} + \frac{e ^{\frac{x}{3}} x u ^{'} ( x )}{3}

= \frac{e ^{\frac{x}{3}} H ( x )}{9} + \frac{e ^{\frac{x}{3}} x u ^{'} ( x )}{3}

e x p an d (x^{2} - y^{2}) (e^{- x^{2} - y^{2}})

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

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

e x p an d (x - 2) (\cdot + 2)

e x p an d \frac{8 a ^{2} b - 32 b ^{3}}{x ^{2} + 2 ( a - 2 b ) x - 8 ab}