If f(x)=|U| then (f(x))^2=U^2 and differentiating we have:
2f(x)f'(x)=2UU'
f'(x)=UU'/f(x)=UU'/|U|. Therefore f'(x)=-U' or U'. Whether this is positive or negative will depend on x. There is also the possibility that the derivative is undefined for particular values of x where U=0.
EXAMPLE
U=3-2x. The graph of U is V-shaped. When x=3/2, U=0 so f(x)=0 and f'(x) is not defined at x=3/2.
When x<3/2 the gradient U'=-2 and when x>3/2 U'=2.