  Differentiability of semigroups is useful for many applications. Here we
focus on stochastic differential equations whose diffusion coefficient is the
square root of a differentiable function but not differentiable itself. For
every $m\in\{0,1,2\}$ we establish an upper bound for a $C^m$-norm of the
semigroup of such a diffusion in terms of the $C^m$-norms of the drift
coefficient and of the squared diffusion coefficient. The constants in our
upper bound are often dimension-independent. Our estimates are thus suitable
for analyzing certain high-dimensional and infinite-dimensional degenerate
stochastic differential equations.
