Lecture

Directional Derivatives: Definition and Applications

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Description

This lecture covers the concept of directional derivatives, starting with the definition and properties. It explains how to calculate directional derivatives and their applications in differentiating functions. The lecture also includes examples illustrating the computation of directional derivatives in various scenarios.

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Ontological neighbourhood

Mathematics

Analysis: Calculus

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In mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

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