Math Problem Statement
find dy/dx by implicit differentiation x^4+x^2y^2+y^3=5
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Calculus
Chain Rule
Product Rule
Formulas
d/dx(x^4) = 4x^3
d/dx(x^2 y^2) = x^2 (2y dy/dx) + y^2 (2x)
d/dx(y^3) = 3y^2 dy/dx
dy/dx = - (4x^3 + 2x y^2) / (2x^2 y + 3y^2)
Theorems
Chain Rule
Product Rule
Suitable Grade Level
Grades 11-12 or early college (Calculus 1)
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