What we have here is a function within a function; x^2+2x-1 is under the radical (sqrt()) sign. That means we have to use the chain rule to differentiate, which says that you take the derivative of the "inside" function (in this case x^2+2x-1) and multiply it by the derivative of the whole function.
Begin by finding the derivative of x^2+2x-1. Using the power rule, the derivative is 2x+2. Now onto the whole function. Note that we can write sqrt(x^2+2x-1) as (x^2+2x-1)^(1/2). That means we can again apply the power rule:
d/dx(x^2+2x-1)^(1/2) = 1/(2(x^2+2x-1)^(1/2))
Now we can multiply this by the derivative of the inside function, which we found as 2x+2. Performing this operation yields:
1/(2(x^2+2x-1)^(1/2))*2x+2 = (2x+2)/(2(x^2+2x-1)^(1/2))
Finally, look for any ways to simplify the problem. We see that there is a 2 in the denominator - is there any way we can get rid of it? In fact, there is by factoring out a 2 from the numerator; take a look:
(2(x+1))/(2(x^2+2x-1)^(1/2)) = (x+1)/((x^2+2x-1)^(1/2))
Because the problem was given to us in radical form, we should convert it back, rewriting the answer as:
(x+1)/(sqrt(x^2+2x-1))
