Question

Find `bb(dy/dx)` in the following:

xy + y² = tan x + y

Answer 1

xy + y² = tan x + y

Differentiating both sides with respect to x,

⇒ `x d/dx (y) + y d/dx (x) + d/dx (y^2) = d/dx (tan x) + d/dx (y)`

⇒ `x dy/dx + y + 2y dy/dx = sec^2 x + dy/dx`

⇒ `dy/dx (x+ 2y - 1) = sec^2 x - y`

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