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

`(dy)/(dx)=-(y+1)/(x+1)`

Explanation:

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

Differentiate both sides with respect to x

`x(dy)/(dx)+y+1+(dy)/(dx)=0`

Take y and 1 to other sides of the equation

`x(dy)/(dx)+(dy)/(dx)=-y-1`

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

`(dy)/(dx)(x+1)=-y-1`

Divide both sides by (x+1)

`(dy)/(dx)=(-y-1)/(x+1)\\\\(dy)/(dx)=-(y+1)/(x+1)`