Following the hint, we have
f ′ ( x ) = x 2 ⋅ 1 − ( x − 1 ) 2 x ( x 2 ) 2 = 2 x − x 2 x 4 = 2 − x x 3 . {\displaystyle f'(x)={\frac {x^{2}\cdot 1-(x-1)2x}{(x^{2})^{2}}}={\frac {2x-x^{2}}{x^{4}}}={\frac {2-x}{x^{3}}}.}
Thus, f ′ ( x ) = 2 − x x 3 . {\displaystyle \color {blue}f'(x)={\frac {2-x}{x^{3}}}.}
