Math Problem Statement

Find the first and second derivatives of various functions, including specific calculations such as f'(x), f''(x), and evaluating the derivative at specific points.

Solution

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Math Problem Analysis

Mathematical Concepts

Derivatives
Polynomial Functions
Chain Rule
Product Rule

Formulas

f'(x) = lim(h→0) [f(x+h) - f(x)] / h
f'(x) = nx^(n-1) (for polynomial terms)
Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)

Theorems

Fundamental Theorem of Calculus
Power Rule
Chain Rule
Product Rule

Suitable Grade Level

Grades 11-12

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