Math Problem Statement

Use logarithmic differentiation to find the derivative of the function.

y = (ex cos2(x))/(4x2 + 5x + 6)

Solution

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Math Problem Analysis

Mathematical Concepts

Logarithmic Differentiation
Implicit Differentiation
Exponential Functions
Trigonometric Functions
Quotient Rule

Formulas

ln(a / b) = ln(a) - ln(b)
ln(a^n) = n * ln(a)
d/dx[ln(y)] = (1/y) * dy/dx
d/dx[cos(x)] = -sin(x)
d/dx[tan(x)] = sec^2(x)

Theorems

Properties of Logarithms
Derivative Rules for Trigonometric Functions
Derivative Rules for Exponential Functions

Suitable Grade Level

Grades 11-12 / Early College