Math Problem Statement

  1. Find all second partial derivatives of f(x, y) = e^ xy sin x

Solution

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Math Problem Analysis

Mathematical Concepts

Partial Derivatives
Multivariable Calculus
Differentiation Rules

Formulas

f_x = ∂f/∂x
f_y = ∂f/∂y
f_{xx} = ∂²f/∂x²
f_{yy} = ∂²f/∂y²
f_{xy} = ∂²f/∂x∂y

Theorems

Mixed Derivatives Theorem (f_{xy} = f_{yx})

Suitable Grade Level

University-level Calculus