How do you find the derivative of y=√x using the definition of derivative?

Lim (√ (x+h) - √x) / h)) * (√ (x+h) + √x)) / (√ (x+h) + √x)) rationaize = (x+h-x) / (h * (√ (x+h) + √x)) = 1 / (√ (x+h) + √x)) replacing h=0 from the lim you get = 1 / (√x+√x) = 1 / (2√x)