Question

Find the derivative of the function. y=6x−8

Answer 1

`\displaystyle y' = 6`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:
`\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)`

Derivative Property [Addition/Subtraction]:
`\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]`

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

`\displaystyle y = 6x - 8`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[6x] - (d)/(dx)[8]`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = 6 (d)/(dx)[x] - (d)/(dx)[8]`
3. Basic Power Rule:
   `\displaystyle y' = 6`

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

Unit: Differentiation