Essential Mathematical Skills and Techniques-Semester 1 Differentiation

The document is a set of lecture notes on differentiation for Semester 1, covering multiple courses (MAS140, MAS151, MAS152, MAS156, and MAS161) at the University of Sheffield. It provides a detailed introduction to differentiation, including definitions, rules (product, quotient, chain, and inverse function rules), and applications, such as finding maxima, minima, and points of inflection. The notes also discuss the relationship between continuity and differentiability, illustrated with examples like the modulus function. A comprehensive list of useful derivatives for various functions, including trigonometric, hyperbolic, and inverse functions, is included. The material is designed to supplement video lectures and is accessible via the course webpage, offering students a solid foundation in differentiation for engineering and mathematical applications.