Question "Fluid Mechanics(Robert Granger)" fluid Velocity comp.

Chapter 4. eq. 4.28- 4.30

u = u0 + (x - x0)(du/dx) + (y - y0)(du/dy) + (z - z0)(du/dz)

v= ...

w = ...


Then with out any significance explanation these equation take a form of
eq 4.31 - 4.33


u = u0 + 1/2 [(x - x0)(du/dx - du/dx ) + (y - y0)(du/dydx - dv/dx) + (z - z0)(du/dz - dw/dx)] ......

v= ...

w = ...


what does this 1/2 in second set of equation means ?

Thank you.