Differentiating Polynomial–Trigonometric Functions Using the Product Rule | (Ep 3)

This tutorial details the process for differentiating functions that combine a polynomial term and a trigonometric term using the calculus Product Rule. The content serves as an introductory guide, focusing on breaking down each differentiation step clearly for educational purposes. Specifically, the lesson demonstrates the application of the Product Rule to the sample function $y = x \cdot \sin(2x)$, illustrating how to handle composite functions within the differentiation process. The instruction aims to build foundational understanding for students in calculus, mathematics, and related engineering studies concerning derivatives of product-based functions.

Central to the explanation is a step-by-step walkthrough of the differentiation of $x \sin(2x)$, including the necessary application of the Chain Rule where applicable to the trigonometric component. The presentation covers the mechanics of applying the Product Rule to these mixed expressions, offering a thorough method for solving related derivative problems encountered in academic settings.