calculus
posted by John .
find the limit of f'(x) = 1/(√x) using the limit definition of derivative as x approaches 0.

Given f(x)=1/√x
f'(x)
=Lim h>0 (f(x+h)f(x))/h
=Lim h>0 (1/√(x+h)1/√x))/h
subtract with common denominator
=Lim h>0 ((√x√(x+h)/(h(√x √(x+h)))
multiply by conjugate of numerator, √(x)+√(x+h)
=Lim h>0 (x(x+h))/(h(√x √(x+h))*(√x+&radic(x+h)))
subtract and cancel h
=Lim h>0 1/(√x √(x+h)*(√x+&radic(x+h)))
Take limit h>0
=1/x^{3/2}