Question

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

Answer 1

Answer:

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

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Derivative Property [Multiplied Constant]:                                                           $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Step-by-step 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