Question

from first principle , find the derivative of y = x³ + 3x² - 5x

Answer 1

Answer:

y' = 3x² + 6x - 5

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

Step-by-step explanation:

Step 1: Define

Identify

y = x³ + 3x² - 5x

Step 2: Differentiate

1. Basic Power Rule:                                                                                             y' = 3x³⁻¹ + 2 · 3x²⁻¹ - 1 · 5x¹⁻¹
2. Simplify:                                                                                                             y' = 3x² + 6x - 5

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

Unit: Derivatives

Book: College Calculus 10e