Question

What is the derivative of f(x)= 2x cubed?

Answer 1

`\displaystyle f'(x) = 6x^2`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

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

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

`\displaystyle f(x) = 2x^3`

Step 2: Differentiate

1. Basic Power Rule [Derivative Rule - Chain Rule]:
   `\displaystyle f'(x) = 6x^2`

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

Unit: Differentiation