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Question
Find `dy/dx` in the following:
xy + y2 = tan x + y
Solution
Since, 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)`
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