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The document is a study guide on partial differentiation, likely part of a first-semester mathematics course such as MAS152: Essential Mathematical Skills and Techniques. It introduces the concept of functions of multiple variables, focusing on two-variable functions like \( z = f(x, y) \), and explains how to compute partial derivatives with respect to each variable while holding the others constant. The guide includes examples of finding first and second-order partial derivatives, using rules like the **product rule** and chain rule. It also covers higher-order derivatives and their notations, such as \( \frac{\partial^2 f}{\partial x^2} \) and \( \frac{\partial^2 f}{\partial x \partial y} \). The document is practical, with step-by-step solutions and graphical interpretations, making it a valuable resource for understanding multivariable calculus.
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