Math Problem Statement

If f(x)=4sinx3+cosx\frac{4\sin x}{3+\cos x}, then f'(x)f′(x) =   

f'(3)f′(3) = 

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Trigonometry
Derivatives
Quotient Rule

Formulas

Quotient rule: \( \left( \frac{g(x)}{h(x)} \right)' = \frac{g'(x)h(x) - g(x)h'(x)}{(h(x))^2} \)
Trigonometric identity: \( \sin^2 x + \cos^2 x = 1 \)

Theorems

Quotient Rule
Trigonometric Identities

Suitable Grade Level

Grades 11-12, Early College