Math Problem Statement

For some constant k, find dy/dx . (a) e^xy + cos(y^3) = kx

Solution

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Math Problem Analysis

Mathematical Concepts

Implicit Differentiation
Product Rule
Chain Rule
Exponential Functions
Trigonometric Functions

Formulas

Product rule: d(uv)/dx = u(dv/dx) + v(du/dx)
Chain rule: d(f(g(x)))/dx = f'(g(x)) * g'(x)
Exponential derivative: d(e^u)/dx = e^u * du/dx
Derivative of cos(u): d(cos(u))/dx = -sin(u) * du/dx

Theorems

Implicit Differentiation
Product Rule
Chain Rule

Suitable Grade Level

College-level calculus