Question

What is the derivative of x cubed?

Answer 1

`\displaystyle (dy)/(dx)[x^3] = 3x^2`

General Formulas and Concepts:

Calculus

Differentiation

• Derivatives
• Derivative Notation

Basic Power Rule:

1. f(x) = cxⁿ
2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

`\displaystyle y = x^3`

Step 2: Differentiate

1. Basic Power Rule:
   `\displaystyle y' = 3x^(3 - 1)`
2. Simplify:
   `\displaystyle y' = 3x^2`

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

Unit: Differentiation