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Question
Find `dy/dx` in the following.
x3 + x2y + xy2 + y3 = 81
Solution
Since, x3 + x2y + xy2 + y3 = 81
Differentiating both sides with respect to x,
`d/dx (x^3) + {x^2 dy/dx + y d/dx (x^2)} + {x dy/dx (y^2) + y^2 d/dx (x)} d/dx (y^3) = d/dx (81)`
`=> 3 x^2 + x^2 dy/dx + y xx 2x + x. 2y dy/dx + y^2 xx 1 + 3y^2 dy/d" = 0`
`=> x^2 dy/dx + x. 2y dy/dx + 3y^2 dy/dx = -(3 x^2 + 2xy + y^2)`
`dy/dx = (- (3 x^2 + 2xy + y^2))/( x^2 + 2xy + 3y^2)`
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