Question

Find `bb(dy/dx)` in the following:

x³ + x²y + xy² + y³ = 81

Answer 1

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 xx 2y dy/dx + y^2 xx 1 + 3y^2 dy/d" = 0`

⇒ `x^2 dy/dx + x xx 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)`