What is expand (5x+y^2)dx+y(2x-x^2)dy ?

The solution to expand (5x+y^2)dx+y(2x-x^2)dy is 5xdx+y^2dx+2xydy-x^2ydy

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expand (5x+y^2)dx+y(2x-x^2)dy

expand

(5 x + y^{2}) d x + y (2 x - x^{2}) d y

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

Solution steps

(5 x + y^{2}) d x + y (2 x - x^{2}) d y

Expand

d x (5 x + y^{2}) : 5 x d x + y^{2} d x

= 5 x d x + y^{2} d x + y (2 x - x^{2}) d y

Expand

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

= 5 x d x + y^{2} d x + 2 x y d y - x^{2} y d y

\frac{( 9 y ^{4} + 3 x ^{3} - 6 x ^{2} y + x ^{2} )}{( x y ^{2} )}

(2 x + 2)^{7}

\frac{1}{( 1 + 3 x ) ^{2}}

\frac{d}{d x} (\frac{2 y + 4 y ^{2} - x ( 2 x - 1 )}{x})

\frac{( n + 1 ) ( n + 2 )}{6}

What is expand (5x+y^2)dx+y(2x-x^2)dy ?
The solution to expand (5x+y^2)dx+y(2x-x^2)dy is 5xdx+y^2dx+2xydy-x^2ydy