Math Problem Statement

Find the derivatives of the given functions shown in the provided image.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Chain Rule
Quotient Rule
Trigonometric Functions
Exponential Functions

Formulas

Power rule: d/dx [x^n] = n*x^(n-1)
Chain rule: d/dx [f(g(x))] = f'(g(x)) * g'(x)
Quotient rule: d/dx [u/v] = (v*u' - u*v')/v^2
Trigonometric derivatives: d/dx [sin(x)] = cos(x), d/dx [cos(x)] = -sin(x)

Theorems

Fundamental Theorem of Calculus
Differentiation Rules

Suitable Grade Level

Grades 11-12, Early College