erweitern (8x^2y^3+6x)*(8xy^3+12x^2y^2y'(x)+3)

Lösung

erweitern

(8 x^{2} y^{3} + 6 x) \cdot (8 x y^{3} + 12 x^{2} y^{2} y^{'} (x) + 3)

64 x^{3} y^{6} + 96 x^{4} y^{5} y' (x) + 72 x^{2} y^{3} + 72 x^{3} y^{2} y' (x) + 18 x

Schritte zur Lösung

(8 x^{2} y^{3} + 6 x) (8 x y^{3} + 12 x^{2} y^{2} y^{'} (x) + 3)

Setze Klammern

= 8 x^{2} y^{3} \cdot 8 x y^{3} + 8 x^{2} y^{3} \cdot 12 x^{2} y^{2} y^{^{'}} (x) + 8 x^{2} y^{3} \cdot 3 + 6 x \cdot 8 x y^{3} + 6 x \cdot 12 x^{2} y^{2} y^{^{'}} (x) + 6 x \cdot 3

= 8 \cdot 8 x^{2} x y^{3} y^{3} + 8 \cdot 12 x^{2} x^{2} y^{3} y^{2} y^{^{'}} (x) + 8 \cdot 3 x^{2} y^{3} + 6 \cdot 8 xx y^{3} + 6 \cdot 12 x^{2} x y^{2} y^{^{'}} (x) + 6 \cdot 3 x

Vereinfache

8 \cdot 8 x^{2} x y^{3} y^{3} + 8 \cdot 12 x^{2} x^{2} y^{3} y^{2} y^{'} (x) + 8 \cdot 3 x^{2} y^{3} + 6 \cdot 8 xx y^{3} + 6 \cdot 12 x^{2} x y^{2} y^{'} (x) + 6 \cdot 3 x : 64 x^{3} y^{6} + 96 x^{4} y^{5} y^{'} (x) + 72 x^{2} y^{3} + 72 x^{3} y^{2} y^{'} (x) + 18 x

= 64 x^{3} y^{6} + 96 x^{4} y^{5} y^{'} (x) + 72 x^{2} y^{3} + 72 x^{3} y^{2} y^{'} (x) + 18 x

e x p an d \frac{6 x}{( x + 2 ) ( x ^{2} - 3 x + 1 )}

e x p an d \frac{5}{x ( 3 x + 1 )}

e x p an d 2 - x (2 sin (4 x) - x (3 cos (4 x) + 13))

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

\frac{d ^{2}}{d x ^{2}} ((y) (sin (x) + cos (x)))