F(x) = (x+3)(2x²+5)
Find the derivative

f'(x) = 6x² + 12x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right

Distributive Property

Algebra I

Terms/Coefficients/Degrees

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Product Rule:

Step-by-step explanation:

Step 1: Define

f(x) = (x + 3)(2x² + 5)

Step 2: Differentiate

Product Rule [Basic Power Rule]:                                                                 f'(x) = (1 · x¹⁻¹ + 0)(2x² + 5) + (x + 3)(2 · 2x²⁻¹ + 0)[Derivative] Simplify:                                                                                       f'(x) = (1)(2x² + 5) + (x + 3)(4x)[Derivative] Multiply:                                                                                       f'(x) = 2x² + 5 + (x + 3)(4x)[Derivative] Distribute:                                                                                     f'(x) = 2x² + 5 + 4x² + 12x[Derivative] Combine like terms:                                                                   f'(x) = 6x² + 12x + 5