Math Problem Statement

Реши задание

Match the derivatives of functions with the correct options based on the given formulas.

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Exponential Functions
Logarithmic Functions
Trigonometric Functions
Inverse Trigonometric Functions

Formulas

Power Rule: (x^n)' = n * x^(n-1)
Exponential Derivative: (e^x)' = e^x
Logarithmic Derivative: (ln x)' = 1/x
Trigonometric Derivatives: (sin x)' = cos x, (cos x)' = -sin x
Inverse Trigonometric Derivatives: (arcsin x)' = 1/sqrt(1-x^2)

Theorems

Fundamental Theorem of Calculus
Chain Rule for Differentiation

Suitable Grade Level

Grades 10-12 (Calculus Level)