For simplicity, dy/dx means f'(x); We have y = ( 8 - x^2 ) / 2x; Then, y = 4/x - x/2; So, f'(x) = (4/x - x/2)' = (4/x)' - (x/2)' = -4/(x^2) -1/2 because we use <span> d<span>ifferentiation formulas, such as : (f+g)' = f' + g'; (cf)' = cf'; x'=1; (1/x)' = -1/(x^2); </span></span>Finally, f'(4) = -4/16 -1/2 = -4/16 - 8/16 = -12/16 = -3/4. The correct answer is E.
