Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Directional Derivatives
Gradient
Multivariable Calculus
Unit Vectors

Formulas

Directional derivative formula: D_uF = ∇F · u
Gradient of a function: ∇F(x, y) = (∂F/∂x, ∂F/∂y)
Unit vector formula: u = (cosθ, sinθ)

Theorems

Directional Derivative Theorem
Gradient Theorem

Suitable Grade Level

Undergraduate Calculus