Answer:
[tex]\displaystyle y' = 9x^2[/tex]
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Derivative Property [Addition/Subtraction]: [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = 3x^3 + 2[/tex]
Step 2: Differentiate
- Derivative Property [Addition/Subtraction]: [tex]\displaystyle y' = \frac{d}{dx}[3x^3] + \frac{d}{dx}[2][/tex]
- Rewrite [Derivative Property - Multiplied Constant]: [tex]\displaystyle y' = 3 \frac{d}{dx}[x^3] + \frac{d}{dx}[2][/tex]
- Basic Power Rule: [tex]\displaystyle y' = 9x^2[/tex]
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
