erweitern dx((x^2-3x+2)*(2x^3+1))

Lösung

erweitern

d x ((x^{2} - 3 x + 2) \cdot (2 x^{3} + 1))

2 x^{5} d x + x^{2} d x - 6 x^{4} d x - 3 x d x + 4 x^{3} d x + 2 d x

Schritte zur Lösung

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

Entferne die Klammern:

(a) = a

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

Multipliziere aus

(x^{2} - 3 x + 2) (2 x^{3} + 1) : 2 x^{5} + x^{2} - 6 x^{4} - 3 x + 4 x^{3} + 2

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

Multipliziere aus

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

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

e x p an d \frac{k}{( s - 3 ) ( s + 11 )}

\frac{\partial}{\partial x} ((y) (3 x^{2} + y^{2} x + y))

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

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

e x p an d \frac{6 x}{( 5 + 3 x ^{2} ) ^{4}}