Question

What is the derivative of 4x+ k​

Answer 1

Answer:

$\displaystyle \frac{dy}{dx} = 4$

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:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

*Note:

Treat k as an arbitrary constant.

Step 1: Define

Identify

$\displaystyle y = 4x + k$

Step 2: Differentiate

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

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

Unit: Differentiation