Derivatives and Their Applications

Calculus serves as an essential tool in machine learning, and understanding derivatives is important for grasping how models learn and adapt. This chapter talks about derivatives, looking into their fundamental role in analyzing and optimizing functions that support machine learning algorithms.

You will start with the basics of differentiation, learning how to compute derivatives of common functions and interpret their meanings. We'll then progress to more complex applications such as the chain rule, which enables the differentiation of composite functions, essential for backpropagation in neural networks. Additionally, you'll learn about partial derivatives, a critical component in understanding how changes in multiple input variables influence a function's output, particularly relevant in multivariable calculus.

Moreover, this chapter examines how derivatives help with optimization techniques like gradient descent, a foundation in training machine learning models. By the end, you'll have the mathematical tools to not only compute derivatives but also apply them effectively in creating models that learn from data.