Verified answer

sqrt x = x^(1/2)

(1/2) * x ^ (1/2 - 1) =

(1/2) * x^(-1/2) =

1 / ( 2 * sqrt(x) ) dx

Pretend for example that you are doing an eaiser problem such as x^2 you know that just becomes 2x for the derivative.

if you do the same thing in the actual problem you are working on it is much easier.

The square root of x is the same as x^1/2 so

(1/2)x^(-1/2) is the answer to the problem

if you are unsure as to why this is the answer think about how you in the first example I showed you brought the 2 down and then the number that is left as the exponent in the number you brought down minus 1 which in that example it was 1. Now in the problem you are trying to solve you has an exponent of 1/2 you bring that down and then what is (1/2)-1 it is (-1/2).

radical x is the same thing as x to the power of 1/2

so you bring the exponent to the front and subtract 1 to get the new exponent.

answer:

(1/2)x^(-1/2)

f(x)=√x

f´(x)=1/2(x^(1-1/2))

f´(x)=1/2(x^-1/2)