Analyse 2: Rules of Calculation: Addition

This lecture covers the rules of calculation for Taylor polynomials, aiming to simplify derivative calculations and utilize established results. By applying the addition rule, one can significantly simplify the process of computing derivatives of rational functions. The lecture also delves into the calculation of Taylor polynomials for exponential functions, showcasing how to add or subtract the Taylor polynomials to find those of hyperbolic functions. Additionally, it explores the properties of even and odd functions, highlighting how their derivatives behave at specific points. The composition rule for differentiable functions is also discussed, emphasizing the importance of understanding these rules in mathematical analysis.