Question

If x√(1 + y) + y√(1 + x) = 0, (x ≠ y), then prove that dy/dx = - 1/(1 + x)².

Answer 1

Given equation is x√(1 + y) + y√(1 + x) = 0

where x ≠ y, we first convert the given equation into y = f(x) form

Clearly, x√(1 + y) = - y√(1 + x)

On squaring both sides, we get

On differentiating both sides w.r.t. x, we get