`x^(3) + x^(2)y+ xy^(2) + y^(3) = 81` – InterviewSolution

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1.	`x^(3) + x^(2)y+ xy^(2) + y^(3) = 81`
Answer» `x^(3) + x^(2)y+ xy^(2) + y^(3) = 81` Differentiate both sides w.r.t. x `3x^(2) + (x^(2)(dy)/(dx)+2xy)` ` + (2xy (dy)/(dx)+y^(2))+ 3y^(2)(dy)/(dx)=0` `rArr (x^(2) + 2xy + 3xy^(2))(dy)/(dx)=-(3x^(2)+2xy+y^(2))` `rArr (dy)/(dx)=-((3x^(2)+2xy+y^(2)))/((x^(2) + 2xy+ 3y^(2)))`

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