We prove our main results by using the time scales

chain rule, the time scales integration by parts formula, the time scales Taylor formula, and classical as well as time scales versions of Holder's inequality.

AD provides a set of mathematically well-defined differentiation rules (symbolic partial derivatives of built-in functions combined with the

chain rule of differential calculus) for transforming a given simulation program into computer code for computing sensitivities.

By recursive application of the

chain rule, the error term for each layer is first calculated.

Chain Rule for Fractional Calculus and Fractional Complex Transform

290, Theorem 2] discovered a fundamental relation from which he deduced the generalized

chain rule for the fractional derivatives.

and using the

chain rule and the fundamental theorem of calculus, we obtain

Using

chain rule:

Chain rule gives the derivative of the composition

Students have experienced difficulty in understanding and using the

chain rule. This study aims at assisting the students to understand and apply the

chain rule and thus inform the author's teaching for future learning of students.

The gradient vector of parameters respect to error function can be obtained by

chain rule in which the optimum values of parameters are determined by iterative algorithms.

For any two [C.sup.1]-functions f and g for which f o g is defined, it is easy to see that the following

chain rule holds, where z = g([zeta]):

The derivative of a composite function, taken with the

chain rule is one of the important notions in calculus.