Math Problem Statement

differentiate y = xarctan(5x)

Solution

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Math Problem Analysis

Mathematical Concepts

Differentiation
Product Rule
Chain Rule
Inverse Trigonometric Functions

Formulas

Product Rule: d/dx[f(x)g(x)] = f'(x)g(x) + f(x)g'(x)
Chain Rule: d/dx[f(g(x))] = f'(g(x)) * g'(x)
Derivative of arctan(x): d/dx[arctan(x)] = 1 / (1 + x^2)

Theorems

Product Rule for differentiation
Chain Rule for composite functions

Suitable Grade Level

Grades 11-12 or early college