finf y'' by implict differentiation

Question

√x + √y = 1

Answer 1

√x+√y = 1
differentiate with respect to x:

1/(2√x) + (1/2√y) dy/dx =0

Substitute √y by 1-√x:
1/(2√x) + (1/2(1-√x)) dy/dx =0

Solve for dy/dx.