Math Problem Statement
Compute the directional derivative of the function f(x,y,z)=x^2y+x√(1+z) at the point (1,2,3) in the direction of the vector ⟨2,1,−2⟩. Round your answer to two decimal places if necessary. Answer = ?
Solution
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Math Problem Analysis
Mathematical Concepts
Directional Derivative
Gradient Vector
Vector Calculus
Formulas
Directional Derivative: D_uf = ∇f · u
Gradient Vector: ∇f = ⟨∂f/∂x, ∂f/∂y, ∂f/∂z⟩
Normalization of Vector: u = v/||v||
Theorems
Gradient Theorem
Chain Rule in Multivariable Calculus
Suitable Grade Level
Undergraduate Calculus
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