quastion about derivative - part 2

[sdahan12]

hi,
in part 2 there is a calculation of dzdx_empirical ,
can somone help and explain the calculation? why is there a sum? and why is there a division by eta and not a division by etx*ex (as i expected to be)?

thanks!

% Check the derivative numerically
ex = randn(size(x), 'single') ;
eta = 0.0001 ;
xp = x + eta * ex ;
yp = vl_nnconv(xp, w, []) ;

dzdx_empirical = sum(dzdy(:) .* (yp(:) - y(:)) / eta) ;
dzdx_computed = sum(dzdx(:) .* ex(:)) ;

fprintf(...
'der: empirical: %f, computed: %f, error: %.2f %%\n', ...
dzdx_empirical, dzdx_computed, ...
abs(1 - dzdx_empirical/dzdx_computed)*100) ;