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

y' = 3x² + 6x - 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

FunctionsFunction 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

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

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

Unit: Derivatives

Book: College Calculus 10e

40 because it’s just a little longer than 32 feet