If we write x in power form x12 , we see that the square root is a function having the appearance of xn and its derivative is therefore equal to
fx=ddxx=ddxx12=21x21−1=21x−21
The answer can also be written as
fx=12x
because x−21=x21−1=x−1=1x
x 
2 
x
=ddxx=ddxx12=21x21−1=21x−21 x=12x 
x21
−1=x−1=1x 