4. xy + y2-tan x + y

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Solution

The given equation is,

xy+ y 2 =tanx+y

Differentiate on both sides of the equation.

d( xy+ y 2 )=d( tanx+y ) d( xy )+d( y 2 )=d( tanx )+dy xdy+ydx+2ydy= sec 2 xdx+dy xdy+2ydy−dy= sec 2 xdx−ydx

Further solve the equation.

( x+2y−1 )dy=( sec 2 x−y )dx dy dx = sec 2 x−y x+2y−1

Thus, the derivative of xy+ y 2 =tanx+yis dy dx = sec 2 x−y x+2y−1 .

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