Question

`(dy)/(dx)` of `xy + y^2 = tan x + y` is

Options

• `(sec^2 x - y)/(x + 2y - 1)`

• `(sec^2x)/(x + 2y)`

• `y/(sec^2x)`

• `(x + 2y)/(sec^2x)`

Answer 1

`(sec^2 x - y)/(x + 2y - 1)`

Explanation:

`xy + y^2 = tan x + y`

Differentiating w.r.t x

`(1 * y + x (dy)/(dx)) + (2y (dy)/(dx)) = sec^2x + (dy)/(dx)`

or `(x + y - 1) (dy)/(dx) = sec^2x - y`

⇒ `(dy)/(dx) = (sec^2x - y)/(x + 2y - 1)`