What is expand (ye^{xy}+2x-1)dx+(xe^{xy}-2y+1)dy ?

The solution to expand (ye^{xy}+2x-1)dx+(xe^{xy}-2y+1)dy is e^{yx}ydx+2xdx-dx+e^{yx}xdy-2ydy+dy

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expand (ye^{xy}+2x-1)dx+(xe^{xy}-2y+1)dy

expand

(y e^{x y} + 2 x - 1) d x + (x e^{x y} - 2 y + 1) d y

e^{y x} y d x + 2 x d x - d x + e^{y x} x d y - 2 y d y + d y

Solution steps

(y e^{x y} + 2 x - 1) d x + (x e^{x y} - 2 y + 1) d y

= (e^{y x} y + 2 x - 1) d x + (e^{y x} x - 2 y + 1) d y

Expand

d x (y e^{x y} + 2 x - 1) : e^{y x} y d x + 2 x d x - d x

= e^{y x} y d x + 2 x d x - d x + (x e^{x y} - 2 y + 1) d y

Expand

d y (x e^{x y} - 2 y + 1) : e^{y x} x d y - 2 y d y + d y

= e^{y x} y d x + 2 x d x - d x + e^{y x} x d y - 2 y d y + d y

(a + i Δ x)^{2}

\frac{d}{d x} ((w (x, y (w, x))) (x^{2} + y (w, x)^{2}))

\frac{1}{( x + 3 ) ^{5}}

(y^{''} (t) + y)^{2}

\frac{2 x + 7}{( x + 3 ) ( x + 4 )}

What is expand (ye^{xy}+2x-1)dx+(xe^{xy}-2y+1)dy ?
The solution to expand (ye^{xy}+2x-1)dx+(xe^{xy}-2y+1)dy is e^{yx}ydx+2xdx-dx+e^{yx}xdy-2ydy+dy