Answer:
\(\displaystyle y' = 6\)
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: \(\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)\)
Derivative Property [Addition/Subtraction]: \(\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]\)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle y = 6x - 8\)
Step 2: Differentiate
- Derivative Property [Addition/Subtraction]: \(\displaystyle y' = \frac{d}{dx}[6x] - \frac{d}{dx}[8]\)
- Rewrite [Derivative Property - Multiplied Constant]: \(\displaystyle y' = 6 \frac{d}{dx}[x] - \frac{d}{dx}[8]\)
- Basic Power Rule: \(\displaystyle y' = 6\)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
