What is expand (xsin(x)+1)dy+(ysin(x)+xycos(x))dx ?

The solution to expand (xsin(x)+1)dy+(ysin(x)+xycos(x))dx is xsin(x)dy+dy+ysin(x)dx+xycos(x)dx

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expand (xsin(x)+1)dy+(ysin(x)+xycos(x))dx

expand

(x sin (x) + 1) d y + (y sin (x) + x y cos (x)) d x

x sin (x) d y + d y + y sin (x) d x + x y cos (x) d x

Solution steps

(x sin (x) + 1) d y + (y sin (x) + x y cos (x)) d x

Expand

d y (x sin (x) + 1) : x sin (x) d y + d y

= x sin (x) d y + d y + (y sin (x) + x y cos (x)) d x

Expand

d x (y sin (x) + x y cos (x)) : y sin (x) d x + x y cos (x) d x

= x sin (x) d y + d y + y sin (x) d x + x y cos (x) d x

\frac{1}{x ( 1 - ln ( x ) ) ^{2}}

\frac{1}{( x - 3 ) ( x - 2 )}

(x - 1) ln (x)

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

(x + d x)^{2}

What is expand (xsin(x)+1)dy+(ysin(x)+xycos(x))dx ?
The solution to expand (xsin(x)+1)dy+(ysin(x)+xycos(x))dx is xsin(x)dy+dy+ysin(x)dx+xycos(x)dx