Math Problem Statement

Solution

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Math Problem Analysis

Mathematical Concepts

Partial Derivatives
Exponentials
Multivariable Calculus

Formulas

Partial derivative with respect to x: \( \frac{\partial}{\partial x}(e^{-4x} y^2) = -4 y^2 e^{-4x} \)
Partial derivative with respect to y: \( \frac{\partial}{\partial y}(e^{-4x} y^2) = 2y e^{-4x} \)

Theorems

Rules of differentiation
Chain rule

Suitable Grade Level

Undergraduate-level calculus or advanced high school mathematics