If f(x) = 2 √x, use the definition of derivative to find f′( x )

Answer 1

f(x)=2√x

f'(x)
=lim h->0 2(√(x+h)-√x)/h
=lim h->0 2((x+h)-x)/(h*(√(x+h)+√x))
=lim h->0 2h/(h*(√(x+h)+√x))
=lim h->0 2/(√(x+h)+√x)
=2/(2√x)
=1/√x