Math Problem Statement

Let y^3+x^2y^5=e^4x. Use implicit differentiation to find a formula for dy/dx

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Chain Rule
Product Rule
Exponential Functions

Formulas

Implicit differentiation: d/dx(f(y)) = f'(y) dy/dx
Product rule: d/dx(uv) = u'v + uv'
Chain rule: d/dx(f(g(x))) = f'(g(x)) * g'(x)

Theorems

Chain Rule
Product Rule

Suitable Grade Level

Grades 11-12 (Advanced Calculus)