Question

Find dydx for xy+x+y=6. Differentiate both sides of the equation with respect to x, and then solve for dydx. Do not substitute for y after solving for dydx. Enclose numerators and denominators in parentheses. For example, (a−b)/(1+n).

Answer 1

Answer:

$\frac{dy}{dx}=-\frac{y+1}{x+1}$

Step-by-step explanation:

The given equation is $xy+x+y=6$

Differentiate both sides with respect to x

$x\frac{dy}{dx}+y+1+\frac{dy}{dx}=0$

Take y and 1 to other sides of the equation

$x\frac{dy}{dx}+\frac{dy}{dx}=-y-1$

Factor out dy/dx from the left hand side of the equation

$\frac{dy}{dx}(x+1)=-y-1$

Divide both sides by (x+1)

$\frac{dy}{dx}=\frac{-y-1}{x+1}\\\\\frac{dy}{dx}=-\frac{y+1}{x+1}$