Verified Answer :

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Answer:

\(\displaystyle \frac{dy}{dx}[x^3] = 3x^2\)

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step 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

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