Math Problem Statement

Using Calculus rules, determine the derivative of the following functions: (a) y = √x cos(x2 + 1). (b) y = ln( 3 pe5x + e−2x)

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Product Rule
Chain Rule
Logarithmic Differentiation
Exponential Functions

Formulas

Product rule: d/dx[u(x)v(x)] = u'(x)v(x) + u(x)v'(x)
Chain rule: d/dx[f(g(x))] = f'(g(x))g'(x)
Derivative of ln(u): d/dx[ln(u)] = 1/u * u'(x)

Theorems

Product rule
Chain rule
Logarithmic differentiation

Suitable Grade Level

College Calculus I