erweitern x^{x^x}(x^xln(x)(ln(x)+1)+x^{x-1})

Lösung

erweitern

x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

x^{x + x^{x}} ln^{2} (x) + x^{x + x^{x}} ln (x) + x^{x^{x} + x - 1}

Schritte zur Lösung

x^{x^{x}} (x^{x} ln (x) (ln (x) + 1) + x^{x - 1})

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = x^{x^{x}}, b = x^{x} ln (x) (ln (x) + 1), c = x^{x - 1}

= x^{x^{x}} x^{x} ln (x) (ln (x) + 1) + x^{x^{x}} x^{x - 1}

= x^{x} x^{x^{x}} ln (x) (ln (x) + 1) + x^{x^{x}} x^{x - 1}

Vereinfache

x^{x} x^{x^{x}} ln (x) (ln (x) + 1) + x^{x^{x}} x^{x - 1} : x^{x + x^{x}} ln^{2} (x) + x^{x + x^{x}} ln (x) + x^{x^{x} + x - 1}

= x^{x + x^{x}} ln^{2} (x) + x^{x + x^{x}} ln (x) + x^{x^{x} + x - 1}

e x p an d (13, - 3, 4) x (8, - 4, 3)

e x p an d (a + b x + c x^{2} + d x^{3} + e x^{4})^{2}

e x p an d \frac{( ( a \cdot ( 1 + g ) ^{n} ) \cdot ( 1 - 0.6 a ) ) - 20}{20}

e x p an d \frac{e ^{- 4 s} ( \frac{1}{s ^{2}} + \frac{3}{s} ) - 5}{s ^{2} + 5 s + 8}

e x p an d - \frac{2 x ( - 2 x + 6 ) ^{3}}{81}