\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2014f.00743}
\itemau{Stupel, Moshe; Fraivert, David; Oxman, Victor}
\itemti{Investigating derivatives by means of combinatorial analysis of the components of the function.}
\itemso{Int. J. Math. Educ. Sci. Technol. 45, No. 6, 892-904 (2014).}
\itemab
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.
\itemrv{~}
\itemcc{I45}
\itemut{properties of high-order derivatives; zeroing of derivatives; composite functions}
\itemli{doi:10.1080/0020739X.2013.872306}
\end