  We consider the (unique) mild solution $u(t,x)$ of a 1-dimensional stochastic
heat equation on $[0,T]\times\mathbb R$ driven by time-homogeneous white noise
in the Wick-Skorokhod sense. The main result of this paper is the computation
of the spatial derivative of $u(t,x)$, denoted by $\partial_x u(t,x)$, and its
representation as a Feynman-Kac type closed form. The chaos expansion of
$\partial_x u(t,x)$ makes it possible to find its (optimal) H\"older regularity
especially in space.
