Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Slope of Tangent Line
Equation of Normal Line
Formulas
Implicit differentiation of x^2 + 2xy = y^3
Slope of tangent line: dy/dx = (2x + 2y) / (3y^2 - 2x)
Normal line slope: negative reciprocal of tangent line slope
Theorems
Implicit Differentiation Rule
Product Rule
Slope-Reciprocal Rule
Suitable Grade Level
Grades 11-12, Early Calculus
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