erweitern (2yy'(x)+2y'(x))(x^3+2x-1)

Lösung

erweitern

(2 y y^{'} (x) + 2 y^{'} (x)) (x^{3} + 2 x - 1)

2 x^{3} yy' (x) + 4 x yy' (x) - 2 yy' (x) + 2 x^{3} y' (x) + 4 x y' (x) - 2 y' (x)

Schritte zur Lösung

(2 y y^{'} (x) + 2 y^{'} (x)) (x^{3} + 2 x - 1)

Setze Klammern

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

Wende Minus-Plus Regeln an

+ (- a) = - a

= 2 x^{3} y y^{^{'}} (x) + 2 \cdot 2 x y y^{^{'}} (x) - 2 \cdot 1 \cdot y y^{^{'}} (x) + 2 x^{3} y^{^{'}} (x) + 2 \cdot 2 x y^{^{'}} (x) - 2 \cdot 1 y^{^{'}} (x)

Vereinfache

2 x^{3} y y^{'} (x) + 2 \cdot 2 x y y^{'} (x) - 2 \cdot 1 \cdot y y^{'} (x) + 2 x^{3} y^{'} (x) + 2 \cdot 2 x y^{'} (x) - 2 \cdot 1 y^{'} (x) : 2 x^{3} y y^{'} (x) + 4 x y y^{'} (x) - 2 y y^{'} (x) + 2 x^{3} y^{'} (x) + 4 x y^{'} (x) - 2 y^{'} (x)

= 2 x^{3} y y^{'} (x) + 4 x y y^{'} (x) - 2 y y^{'} (x) + 2 x^{3} y^{'} (x) + 4 x y^{'} (x) - 2 y^{'} (x)

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

e x p an d \frac{19 ( e ^{2} + 3 )}{3}

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

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

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