erweitern (2xy+z^2)dx+(2yz+x^2)dy+(2xz+y^2)dz

Lösung

erweitern

(2 x y + z^{2}) d x + (2 yz + x^{2}) d y + (2 x z + y^{2}) d z

2 x y d x + z^{2} d x + 2 yz d y + x^{2} d y + 2 x z d z + y^{2} d z

Schritte zur Lösung

(2 x y + z^{2}) d x + (2 yz + x^{2}) d y + (2 x z + y^{2}) d z

Multipliziere aus

d x (2 x y + z^{2}) : 2 x y d x + z^{2} d x

= 2 x y d x + z^{2} d x + (2 yz + x^{2}) d y + (2 x z + y^{2}) d z

Multipliziere aus

d y (2 yz + x^{2}) : 2 yz d y + x^{2} d y

= 2 x y d x + z^{2} d x + 2 yz d y + x^{2} d y + (2 x z + y^{2}) d z

Multipliziere aus

d z (2 x z + y^{2}) : 2 x z d z + y^{2} d z

= 2 x y d x + z^{2} d x + 2 yz d y + x^{2} d y + 2 x z d z + y^{2} d z

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

e x p an d 12 (2 - 2) + 54

e x p an d \frac{1}{( x + 4 ) ( x + 5 )}

e x p an d \frac{1}{x} a t (- 2, - \frac{1}{2})

e x p an d y x + 1 - I n (1 + x + 1)