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

The solution to expand (x^2-x+y^2)dx+(2xy+e^{-y})dy is x^2dx-xdx+y^2dx+2xydy+e^{-y}dy

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expand (x^2-x+y^2)dx+(2xy+e^{-y})dy

expand

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

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

Solution steps

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

Expand

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

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

Expand

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

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

(- 3 sin (x) + 3 sin (3 x))^{2} + (3 cos (x) - cos (3 x) \cdot 3)^{2}

\frac{2}{( e ^{x} - e ^{- x} ) ^{2}}

(e^{x} - 2) e^{x}

6 (7 d + \frac{1}{2})

\frac{sin ^{2} ( x )}{( 1 + cos ( x ) ) ^{2}}

What is expand (x^2-x+y^2)dx+(2xy+e^{-y})dy ?
The solution to expand (x^2-x+y^2)dx+(2xy+e^{-y})dy is x^2dx-xdx+y^2dx+2xydy+e^{-y}dy