How to have left and right arrow above and below with an equation with text

Due to the symmetry, an array will do with no other trick:

documentclass{article}
usepackage{amsmath}

begin{document}

[
frac{dI}{dm}=
begin{array}{@{}c@{}}
text{Approach 1} 
$leftarrowfill$
displaystyle
frac{partial f_p(m_{p})}{m_{p}},
frac{partial f_{p-1}(m_{p-1})}{m_{p-1}}
dots
frac{partial f_1(m_{1})}{m_{1}}

$rightarrowfill$
text{Approach 2}
end{array}
]

end{document}

For less generous vertical space use something like

[
renewcommand{arraystretch}{0.75}
frac{dI}{dm}=
begin{array}{@{}c@{}}
text{Approach 1} 
$leftarrowfill$
[...]