Marginal rate of technical substitution for multi-dimension inputs? Suppose I have a vector x = ($x_1,x_2,x_3,x_4,x_5$) of inputs. How it is the MRTS($x_1,x_2,x_3,x_4,x_5$) ?

And which is the relation with the marginal products of inputs 1-5 ?
\begin{equation}
MRTS_{x_{i};x_{j}}=\frac{\partial f(X)}{\partial x_{i}}/\frac{\partial f(X)}{\partial x_{j}} \qquad \forall i\neq j
\end{equation}