$\displaystyle f'(x)= \frac{3}{2x}$\displaystyle f'(x)= \frac{3}{2x}

$\displaystyle f'(x)= \frac{-3x^2-2x+3}{2x}$\displaystyle f'(x)= \frac{-3x^2-2x+3}{2x}

$\displaystyle f'(x)= \frac{-3x^2-2x+3}{\left(x^2+1\right)^2}$\displaystyle f'(x)= \frac{-3x^2-2x+3}{\left(x^2+1\right)^2}

$\displaystyle f'\left(x\right)= \frac{9x^2+2x+3}{\left(x^2+1\right)^2}$\displaystyle f'\left(x\right)= \frac{9x^2+2x+3}{\left(x^2+1\right)^2}