erweitern (4xy+2x^2y)+(2x^2+3y^2)y'(x)

Lösung

erweitern

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

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

Schritte zur Lösung

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

Multipliziere aus

y^{'} (x) (2 x^{2} + 3 y^{2}) : 2 x^{2} y^{'} (x) + 3 y^{'} (x) y^{2}

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

Entferne die Klammern:

(a) = a

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

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

e x p an d 6 (- e^{3 x} (2 sin (2 x) - 3 cos (2 x)))

e x p an d (sec (x) + tan (x))^{3} (sec (x) - tan (x))^{4}

s im pl i f y ((cos (θ) + i sin (θ)))^{3}

e x p an d c H (r (o, s, x), o, s, x) a d r (o, s, x) a d os (x - 2 x = 6)