Question

Differentiate the function:
y=x^3+2x-1

Answer 1

y' = 3x² + 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Algebra I

• Functions
• Function Notation

Calculus

Derivatives

Derivative Notation

Basic Power Rule:

• f(x) = cxⁿ
• f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

y = x³ + 2x - 1

Step 2: Differentiate

1. Basic Power Rule: y' = 3x³⁻¹ + 1 · 2x¹⁻¹ - 0
2. Simplify: y' = 3x² + 2

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Derivatives

Book: College Calculus 10e