Why are they taking the derivative of 1 - x

When taking the derivative of this function, why do they take the derivative of 1 - x in the numerator after using the chain rule on 1 / (sqrt(1 - x)?

http://www.wolframalpha.com/input/?i=4+%2F+sqrt%281-+x%29

The chain rule is used for composite functions. In the example, think of f(x) = 1/sqrt x. Now if g(x) = 1- x, f(g(x)) would be 1/sqrt(1-x). You have to take the derivative of each, so first the derivative of the sqrt, then the inner function 1-x. Another example, what if you had sin (x^2)? The outer derivative would be cos(x^2). No, take the derivative of x^2, you have 2x cos x^2.