Math Problem Statement

The following system of equations defines both u = u(x, y) and v = v(x, y) as twice continuously differentiable functions of x and y around the point P where (x, y, u, v) = (−1, 1, 1, 2): xu3 + v = y2 3uv − x = 7. Answer the following questions.

  1. Find the differentials of u and v expressed in terms of the differentials of x and y

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Multivariable Calculus
Differentials

Formulas

differentiation of a product of functions
implicit differentiation

Theorems

Chain Rule

Suitable Grade Level

Undergraduate Calculus