Question: sqrt(1-x^2) +sqrt (1-y^2) =a (x-y). then find dy/dx ?
Carry out implicit differentiation on the expression, wrt x.
(1/2)(-2x)/sqrt(1-x^2) + (1/2)(-2y)/sqrt(1-y^2).dy/dx = a(1 - dy/dx)
rearranging and solving for dy/dx,
{(-y)/sqrt(1-y^2) + a).dy/dx = a + x/sqrt(1-x^2)
dy/dx = {[a.sqrt(1-x^2) + x][sqrt(1-y^2)]} / {[a.sqrt(1-y^2) - y][sqrt(1 - x^2)]}