How would one use the Table command to create a list of derivatives ? For example, f[x_] := Sqrt[3 + x]/2 ?
Just to acknowledge there are a variety of opinions as to how to help with homework problems.
My suggestion is to first figure out how to do it without the Table command.
Documentation Center or Documentation Center 2
f[x_] := Sqrt[3 + x]/2;
A first derivative:
{D[f[x], x], D[f[x], {x, 1}], f'[x], Derivative[1][f][x]}
A second derivative:
{D[f[x], x, x], D[f[x], {x, 2}], f''[x], Derivative[2][f][x]}
and Yours table 5 of derivatives:
Table[D[f[x], {x, n}], {n, 1, 5}]

Or:
Table[Derivative[n][f][x], {n, 1, 5}]