erweitern (x+xΔ)^3

Lösung

erweitern

(x + x Δ)^{3}

x^{3} + 3Δ x^{3} + 3 Δ^{2} x^{3} + Δ^{3} x^{3}

Schritte zur Lösung

(x + x Δ)^{3}

= (x + Δ x)^{3}

Wende Formel für perfekte dritte Potenzen an:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

a = x, b = x Δ

= x^{3} + 3 x^{2} x Δ + 3 x (x Δ)^{2} + (x Δ)^{3}

Vereinfache

x^{3} + 3 x^{2} x Δ + 3 x (x Δ)^{2} + (x Δ)^{3} : x^{3} + 3Δ x^{3} + 3 Δ^{2} x^{3} + Δ^{3} x^{3}

= x^{3} + 3Δ x^{3} + 3 Δ^{2} x^{3} + Δ^{3} x^{3}

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

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

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

e x p an d 7 (x + Δ x)^{2} - 5 (x + Δ x)

e x p an d \frac{( a + h ) ^{3}}{( a + h ) ^{2} + 1}