Neural Network For Automatic Differentiation Of Quadratic Polynomials

Abstract

This project explores the connection between calculus and artificial intelligence by demonstrating how a neural network can learn the derivative rule of quadratic functions. A quadratic function has the general form f(x)=ax^2+bx+c, and its derivative is f′(x)=2ax+b. In calculus, derivatives represent the rate of change of a function and the slope of the tangent line at any point on a curve. In this project, a dataset of randomly generated quadratic function coefficients (a,b,c) is used as input to train a neural network model. The model learns to map these coefficients to the corresponding derivative coefficients (2a,b). Using Python and TensorFlow, the neural network is trained through regression techniques and activation functions to identify the mathematical relationship between the function and its derivative. The results show that neural networks can successfully learn mathematical patterns and rules from data rather than being explicitly programmed. This project highlights how concepts from calculus can be combined with machine learning to build intelligent systems that recognize and model mathematical relationships.

Research Team