erweitern (3x-2)(3x^2-4x+25)^5dx

Lösung

erweitern

(3 x - 2) (3 x^{2} - 4 x + 25)^{5} d x

729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

Schritte zur Lösung

(3 x - 2) (3 x^{2} - 4 x + 25)^{5} d x

Wende das Distributivgesetz an:

a (b - c) = ab - a c

a = (3 x^{2} - 4 x + 25)^{5} d x, b = 3 x, c = 2

= (3 x^{2} - 4 x + 25)^{5} d x \cdot 3 x - (3 x^{2} - 4 x + 25)^{5} d x \cdot 2

= 3 x (3 x^{2} - 4 x + 25)^{5} d x - 2 (3 x^{2} - 4 x + 25)^{5} d x

Vereinfache

3 x (3 x^{2} - 4 x + 25)^{5} d x - 2 (3 x^{2} - 4 x + 25)^{5} d x : 729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

= 729 x^{11} d x - 5346 x^{10} d x + 46575 x^{9} d x - 208170 x^{8} d x + 961290 x^{7} d x - 2877252 x^{6} d x + 8558798 x^{5} d x - 17126500 x^{4} d x + 33378125 x^{3} d x - 40156250 x^{2} d x + 44921875 x d x - 19531250 d x

e x p an d lo g_{10} (b) (z^{5} x)

e x p an d cosh (t) U (t - 3)

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

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

\frac{\partial}{\partial x} ((f (x, y)) (3 x + y e^{y}))