Math Problem Statement
Let f(x)=xe^x\cos(x). Find f' \left( \frac{\pi}{6} \right). Please enter your answer in decimal form with three digits after the decimal point.
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Product Rule
Trigonometric Functions
Exponential Functions
Formulas
Product rule: d/dx [u(x)v(x)w(x)] = u'(x)v(x)w(x) + u(x)v'(x)w(x) + u(x)v(x)w'(x)
f'(x) = e^x cos(x) + x e^x cos(x) - x e^x sin(x)
Theorems
Product Rule
Basic Derivatives
Trigonometric Derivatives
Suitable Grade Level
Grades 11-12, College Calculus
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