Question

Differentiate each function with respect to x:
F(x)=x/(x+1)^1/2

Answer 1

use the quotient rule

f ' (x) = ( (1)(x+1)^(1/2) - x(1/2)(x+1)^(-1/2) )/(x+1)

= (1/2)(x+1)^(-1/2) (2(x+1) - x )/(x+1)
= (1/2)(x+2)/(x+1)^(3/2)
or
= (x+2)/(2(x+1)^(3/2 )