If `x y+y^2=tanx+y ,t h e nfin d(dy)/(dx)dot`

Explanation

The given relation is `xy+y^(2)=tan x + y.`
Differentiating both sides with respect to x, we get
`(d)/(d)(xy)+(d)/(dx)(y^(2))=(d)/(dx(tan x) +(dy)/(dx)`
`"or "[y.1+x.(dy)/(dx)]+2y(dy)/(dx)=sec^(2) x+(dy)/(dx)`