erweitern 5(x+dx)^4

Lösung

erweitern

5 (x + d x)^{4}

5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

Schritte zur Lösung

5 (x + d x)^{4}

(x + d x)^{4} = x^{4} + 4 x^{3} d x + 6 x^{2} d x^{2} + 4 x d x^{3} + d x^{4}

= 5 (x^{4} + 4 x^{3} d x + 6 x^{2} d x^{2} + 4 x d x^{3} + d x^{4})

Setze Klammern

= 5 x^{4} + 5 \cdot 4 x^{3} d x + 5 \cdot 6 x^{2} d x^{2} + 5 \cdot 4 x d x^{3} + 5 d x^{4}

Vereinfache

5 x^{4} + 5 \cdot 4 x^{3} d x + 5 \cdot 6 x^{2} d x^{2} + 5 \cdot 4 x d x^{3} + 5 d x^{4} : 5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

= 5 x^{4} + 20 x^{3} d x + 30 x^{2} d x^{2} + 20 x d x^{3} + 5 d x^{4}

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

e x p an d L [t^{2}] (s - 3)

e x p an d (L^{t} - L^{- t})^{3}

e x p an d \frac{s ^{2} + 7 - e ^{- π s}}{s ( s ^{2} + 16 )}

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