Math Problem Statement

find the slope of the tangent line to the curve below at the point (7,4) square root of 4x+y + square root of 2xy= 13.14016902304

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Algebra
Radical Functions

Formulas

Implicit Differentiation: d/dx [f(x, y)] = ∂f/∂x + (∂f/∂y) dy/dx
Chain Rule: d/dx [√(u)] = 1/(2√(u)) du/dx

Theorems

Implicit Differentiation Theorem
Chain Rule Theorem

Suitable Grade Level

Grades 11-12 (Advanced High School) or College-level Calculus