What is expand (4xy+3y^2x)dx+x(x+2y)dy ?

The solution to expand (4xy+3y^2x)dx+x(x+2y)dy is 4xydx+3xy^2dx+x^2dy+2xydy

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expand (4xy+3y^2x)dx+x(x+2y)dy

expand

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

4 x y d x + 3 x y^{2} d x + x^{2} d y + 2 x y d y

Solution steps

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

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

Expand

d x (4 x y + 3 y^{2} x) : 4 x y d x + 3 x y^{2} d x

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

Expand

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

= 4 x y d x + 3 x y^{2} d x + x^{2} d y + 2 x y d y

\frac{1}{2} (- lo g_{2} (3) + 1)

- \frac{e ^{n θ} ( - n e ^{- n θ} θ - e ^{- n θ} )}{n}

tan (\frac{π}{3} - x)

(x + 5) (2 x - 35)

lo g_{12} (\frac{y ^{4}}{z m ^{4}})

What is expand (4xy+3y^2x)dx+x(x+2y)dy ?
The solution to expand (4xy+3y^2x)dx+x(x+2y)dy is 4xydx+3xy^2dx+x^2dy+2xydy