Math Problem Statement
Find dy dx by implicit differentiation. x5 − xy + y2 = 8
Solution
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Math Problem Analysis
Mathematical Concepts
Implicit Differentiation
Calculus
Product Rule
Chain Rule
Formulas
d/dx(f(x)g(x)) = f'(x)g(x) + f(x)g'(x) (Product Rule)
d/dx(y^n) = n * y^(n-1) * dy/dx (Chain Rule)
Theorems
Implicit Differentiation Theorem
Product Rule for Derivatives
Chain Rule for Differentiation
Suitable Grade Level
Grades 11-12 or Early College (Calculus)