Answer:
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1-y}{1+x}[/tex]
Step-by-step explanation:
Differentiate xy using the product rule, then
Given
x - y = xy
1 - [tex]\frac{dy}{dx}[/tex] = x. [tex]\frac{dy}{dx}[/tex] + y. 1 = x[tex]\frac{dy}{dx}[/tex] + y ( subtract 1 from both sides )
- [tex]\frac{dy}{dx}[/tex] = x [tex]\frac{dy}{dx}[/tex] + y - 1 ( subtract x [tex]\frac{dy}{dx}[/tex] from both sides )
- [tex]\frac{dy}{dx}[/tex] - x [tex]\frac{dy}{dx}[/tex] = y - 1 ( multiply through by - 1 )
[tex]\frac{dy}{dx}[/tex] + x[tex]\frac{dy}{dx}[/tex] = 1 - y
[tex]\frac{dy}{dx}[/tex] (1 + x) = 1 - y ← divide both sides by (1 + x)
[tex]\frac{dy}{dx}[/tex] = [tex]\frac{1-y}{1+x}[/tex]
