Question

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

x² + xy + y² = 100

Answer 1

x² + xy + y² = 100

Differentiating both sides with respect to x,

⇒ `d/dx (x^2) + {x d/dx (y) + y d/dx (x)} + d/dx (y^2) = d/dx (100)`

⇒ `2x + (x dy/dx + y xx 1) + 2y dy/dx = 0`

⇒ `2x + (x dy/dx + y) + 2y dy/dx = 0`

⇒ `2x + y + x dy/dx + 2y dy/dx = 0`

⇒ `(x + 2y)dy/dx + (2x + y) = 0`

⇒ `(x + 2y)dy/dx = -(2x + y)`

∴ `dy/dx = (-(2x + y))/(x + 2y)`