Math Problem Statement
Find grad f if f=e^xy - xcos(yz^2)
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Gradient
Partial Derivatives
Chain Rule
Product Rule
Formulas
Gradient: ∇f = (∂f/∂x, ∂f/∂y, ∂f/∂z)
Chain Rule: ∂(e^xy)/∂x = y * e^xy, ∂(e^xy)/∂y = x * e^xy
Product Rule: ∂(xcos(yz^2))/∂x = -cos(yz^2), ∂(xcos(yz^2))/∂y = x * sin(yz^2) * z^2
Theorems
Chain Rule
Product Rule
Suitable Grade Level
Undergraduate - Multivariable Calculus
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