#f(x) = (x-1) (x+3)^{-3}#
#f'(x) = frac{d}{dx}( (x-1) (x+3)^{-3} )#
#= (x+3)^{-3} frac{d}{dx}( x-1 ) + (x-1) frac{d}{dx}( (x+3)^{-3} )#
#= (x+3)^{-3} ( 1 ) + (x-1) ( (-3) (x+3)^{-4} (1) )#
#= (x+3)^{-4} ( (x+3) - 3 (x-1) ) #
#= frac{2(3-x)}{(x+3)^{4}}#