  In the 1990's exponential-type error bounds appeared in the theory of radial
basis functions. This kind of error bounds is very powerful. However it only
measures the difference between the approximant and approximand. Mathematicians
and engineers often need to know the matching of the derivatives when dealing
with partial differential equations. In this paper we extend this kind of error
bounds to a form which measures the difference between the derivatives of the
approximant and approximand.
