Differentiate a hard problem

find dy/dx
y = √(x + (√x + (√x)))

y = (x + (x + x^(1/2))^(1/2))^(1/2)
dy/dx = (1/2) * (x + (x + x^(1/2))^(1/2))^(-1/2) * (1/2) * (x + x^(1/2))^(-1/2) * (1/2) * x^(-1/2)
dy/dx = (1/8) * (x + (x + x^(1/2))^(1/2))^(-1/2) * (x + x^(1/2))^(-1/2) * x^(-1/2)

y = √(x + (√x + (√x))) = √(x + 2√x),

squaring both-sides,
y^2 = x + 2√x,

2y.y' = 1 + 1/√x = (√x +1)/√x,

y' = (√x +1) / 2y√x,

y' = (√x+1) / 2√x[(√x +2√x) = (√x+1)/2(x + 2x),

y' = (√x + 1) / 6x >===========================< ANSWER

sqrt(x+sqrt(x)+sqrt(x))
sqrt(x+2sqrt(x))
u=x+2sqrt(x)
du=1+1/sqrt(x)

d/dx(sqrt(u))
1/2u^(-1/2)*du
1/2(x+2sqrt(x))^(-1/2) * (1+1/sqrt(x))

make it a good day

dy/dx = (1 + 1/(2√x) + 1/(2√x))/(2√(x + (√x + (√x)))