erweitern x(x^3+3x^2dx+3xdx^2+dx^3+1)

Lösung

erweitern

x (x^{3} + 3 x^{2} d x + 3 x d x^{2} + d x^{3} + 1)

x^{4} + 3 x^{3} d x + 3 x^{2} d x^{2} + x d x^{3} + x

Schritte zur Lösung

x (x^{3} + 3 x^{2} d x + 3 x d x^{2} + d x^{3} + 1)

Setze Klammern

= x x^{3} + x \cdot 3 x^{2} d x + x \cdot 3 x d x^{2} + x d x^{3} + x \cdot 1

= x^{3} x + 3 x^{2} x d x + 3 xx d x^{2} + x d x^{3} + 1 \cdot x

Vereinfache

x^{3} x + 3 x^{2} x d x + 3 xx d x^{2} + x d x^{3} + 1 \cdot x : x^{4} + 3 x^{3} d x + 3 x^{2} d x^{2} + x d x^{3} + x

= x^{4} + 3 x^{3} d x + 3 x^{2} d x^{2} + x d x^{3} + x

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

e x p an d (5 x^{3} (4 e^{\frac{x}{y}} y^{3} - e^{\frac{x}{y}} x y^{2})) \cdot y

e x p an d \frac{3 ( x + 2 )}{4}

e x p an d \frac{0.5 ( 3 s + 1 )}{3 s ^{2} + s + 2 k}

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