Automatic differentiation is a fundamental tool in the implementation of gradient-based methods in machine learning, enabling efficient and accurate computation of derivatives for complex functions. This paper revisits the classical gradient descent algorithm within the framework of automatic differentiation, illustrating it through a sequence of increasingly intricate examples. In this approach, optimization problems are formulated as computable objective functions, even when the underlying function lacks a closed-form analytical expression in classical mathematics. Gradients are automatically computed, and the gradient descent algorithm is applied without conceptual modification. A central insight is that many seemingly heterogeneous problems can be unified under a single computational framework through appropriate formulation of an objective function. To demonstrate this perspective progressively, four examples of increasing complexity are presented. Linear regression serves as the initial case, offering a familiar setting with a clear analytical form and providing a transparent bridge between gradient descent, automatic differentiation, and foundational machine learning algorithms. Subsequent cases involve problems where classical mathematics lacks explicit or clean formulations, yet naturally arise in computational settings and become tractable through the use of automatic differentiation. The goal of this paper is to present an accessible and inspiring pedagogical exposition that highlights how automatic differentiation can serve as a unifying bridge between classical numerical optimization and modern applications in machine learning—making these concepts accessible and enlightening for students in mathematics and computer science.