Can neural network represent a relation that is a derivative?
Interesting question.

What you are asking for is if a neural network is able to represent and/or approximate functions.

The answer is: Yes, the Neural Networks can represent derivatives of functions.

In this paper, the possibility is explained.

Approximation of functions and their derivatives: A neural network implementation with applications

Other author take the same conclusion:

Multilayer feedforward networks are universal approximators

Generalization and Approximation Capabilities of Multilayer Networks

Approximation Capability of Layered Neural Networks with Sigmoid Units on Two Layers