id: 06361442
dt: j
an: 2014f.00743
au: Stupel, Moshe; Fraivert, David; Oxman, Victor
ti: Investigating derivatives by means of combinatorial analysis of the
components of the function.
so: Int. J. Math. Educ. Sci. Technol. 45, No. 6, 892-904 (2014).
py: 2014
pu: Taylor \& Francis, Abingdon, Oxfordshire
la: EN
cc: I45
ut: properties of high-order derivatives; zeroing of derivatives; composite
functions
ci:
li: doi:10.1080/0020739X.2013.872306
ab: Summary: Given a composite function of the form $h(x) = f(g(x))$,
difficulties are often encountered in calculating the value of the
$n$th derivative at some point $x = x_{0}$ when one attempts to
determine whether its $n$th derivative becomes zero at this point, or
attempts to find the sign of the $n$th derivative by differentiating it
$n$ times and substituting $x_{0}$.{ }This present paper offers an
alternative method that allows the investigation of the $n$th
derivative of function $h(x)$ based on the investigation of functions
$f(x)$ and $g(x)$ only.{ }Several examples are given, which implement
the conclusions on the properties of the relation.
rv: