Question

What is the derivative of 4x+ k​

Answer 1

`\displaystyle (dy)/(dx) = 4`

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:

*Note:

Treat k as an arbitrary constant.

Step 1: Define

Identify

`\displaystyle y = 4x + k`

Step 2: Differentiate

1. Derivative Property [Addition/Subtraction]:
   `\displaystyle y' = (d)/(dx)[4x] + (d)/(dx)[k]`
2. Rewrite [Derivative Property - Multiplied Constant]:
   `\displaystyle y' = 4 (d)/(dx)[x] + (d)/(dx)[k]`
3. Basic Power Rule:
   `\displaystyle y' = 4`

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

Unit: Differentiation