find derivative of square root of -x minus x. (x<0).
the books answer is -1/2-x^1/2-1. how do they keep the negative under the square root sign?
You might want to write the function as:
$\displaystyle f(x)=(-x)^{\frac{1}{2}}-x$
Now differentiate term by term, using the power and chain rules on the first term. The convert back to radical notation. You will then see why the negative stays with the $\displaystyle x$ under the radical.