Solve derivative

If you rewrite your second equation as (1-x)x^0.5, you'll notice it doesn't actually equal the same thing. That's because it was in the bottom of a fraction before, meaning it should have a *negative* derivative.
Also, you forgot about all constants turning into 0 when you take the derivative, meaning the derivative should look a bit more like (0-1)(-0.5)(x^-1.5).

Hope this is able to help! ;)

Here is one suggestion:

$y = \frac{1-x}{x^{0.5}}\\ y = \frac{1}{x^{0.5}}- \frac{x}{x^{0.5}}\\ y=x^{-0.5}-x^{0.5}\\ y'=-0.5x^{-1.5}-0.5x^{-0.5}\\ y'=\frac{-0.5}{x\sqrt x }-\frac{0.5}{\sqrt x}\\ y'=\frac{-1}{2x^{1.5}}(1+x)$

It probably would have been quicker to use the quotient rule.

Note: I have not checked for careless errors.