What is expand y(4x+3y^3)dx+x(2x+5y^3)dx ?

The solution to expand y(4x+3y^3)dx+x(2x+5y^3)dx is 4yxdx+3y^4dx+2x^2dx+5y^3xdx

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expand y(4x+3y^3)dx+x(2x+5y^3)dx

expand

y (4 x + 3 y^{3}) d x + x (2 x + 5 y^{3}) d x

4 y x d x + 3 y^{4} d x + 2 x^{2} d x + 5 y^{3} x d x

Solution steps

y (4 x + 3 y^{3}) d x + x (2 x + 5 y^{3}) d x

Expand

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

= 4 y x d x + 3 y^{4} d x + x (2 x + 5 y^{3}) d x

Expand

x d x (2 x + 5 y^{3}) : 2 x^{2} d x + 5 y^{3} x d x

= 4 y x d x + 3 y^{4} d x + 2 x^{2} d x + 5 y^{3} x d x

(2 (y \cdot v) - 2 y) (d y \cdot v + y \cdot d v)

(4 x + 2 - 2 y, - 3 + 3 y - 3 x) (- y + x + 7)

\frac{x + 1}{( x - 1 ) ( x + 4 )}

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

\frac{7}{( x - 3 ) ^{2}}

What is expand y(4x+3y^3)dx+x(2x+5y^3)dx ?
The solution to expand y(4x+3y^3)dx+x(2x+5y^3)dx is 4yxdx+3y^4dx+2x^2dx+5y^3xdx