Average change rate of f(x) to (x, x+δ x) k = (sqrt (x+δ x)-sqrt (x))/δ x.

The instantaneous rate of change is to find lim (δ x->; 0) the limit of k

Multiply sqrt (x+δ x)+sqrt (x) up and down at the same time.

k =δx/0(sqrt(x+δx)+sqrt(x))δx)= 1/(sqrt(x+δx)+sqrt(x))

lim(δx-& gt； 0) k = 1/2sqrt(x)