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Explore the concept of derivatives in higher dimensions in this 56-minute lecture from the University of Oxford's 2nd Year Mathematics course. Delve into the challenges of extending the classical definition of derivatives to functions of multiple variables, particularly in 3-dimensional space. Discover how the derivative transforms from a scalar quantity to a linear map, serving as the 'best linear approximation' to a function near a given point. Learn how this new understanding allows for the extension of familiar single-variable derivative properties to higher-dimensional scenarios. Build upon the foundations laid in the first lecture of the series, advancing your comprehension of multidimensional analysis and geometry.
