singular locus and jacobian matrix

Question

Let $R=k[x_1, \cdots ,x_r] / I$ be an affine ring over a perfect field $k$ and suppose that $I$ has pure codimension $c$. Suppose that $I= (f_1, \cdots , f_s)$. If $J$ is the ideal of $R$ generated by the $c \times c$ minors of the Jacobian matrix $( \partial f_i / \partial x_j)$ then $J$ defines the sigular locus of $R$ in the sense that a prime $P$ of $R$ contains $J$ iff $R_P$ is not a regular local ring. Please help me to proof it and or refer me to some text