For
1
≤
p
≤
∞
1\leq p\leq \infty
, a one-parameter family of symmetric quantum derivatives is defined for each order of differentiation as are two families of Riemann symmetric quantum derivatives. For
1
≤
p
≤
∞
1\leq p\leq \infty
, symmetrization holds, that is, whenever the
L
p
L^{p}
k
k
th Peano derivative exists at a point, all of these derivatives of order
k
k
also exist at that point. The main result, desymmetrization, is that conversely, for
1
≤
p
≤
∞
1\leq p\leq \infty
, each
L
p
L^{p}
symmetric quantum derivative is a.e. equivalent to the
L
p
L^{p}
Peano derivative of the same order. For
k
=
1
k=1
and
2
2
, each
k
k
th
L
p
L^{p}
symmetric quantum derivative coincides with both corresponding
k
k
th
L
p
L^{p}
Riemann symmetric quantum derivatives, so, in particular, for
k
=
1
k=1
and
2
2
, both
k
k
th
L
p
L^{p}
Riemann symmetric quantum derivatives are a.e. equivalent to the
L
p
L^{p}
Peano derivative.