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If x y+y^2=tanx+y ,then find (dy)/(dx)...

If `x y+y^2`=`tanx+y` ,then find `(dy)/(dx)`

Text Solution

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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)`
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