Answer:
[tex]\frac{dy}{dx}=-\frac{y+1}{x+1}[/tex]
Step-by-step explanation:
The given equation is [tex]xy+x+y=6[/tex]
Differentiate both sides with respect to x
[tex]x\frac{dy}{dx}+y+1+\frac{dy}{dx}=0[/tex]
Take y and 1 to other sides of the equation
[tex]x\frac{dy}{dx}+\frac{dy}{dx}=-y-1[/tex]
Factor out dy/dx from the left hand side of the equation
[tex]\frac{dy}{dx}(x+1)=-y-1[/tex]
Divide both sides by (x+1)
[tex]\frac{dy}{dx}=\frac{-y-1}{x+1}\\\\\frac{dy}{dx}=-\frac{y+1}{x+1}[/tex]
