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What is the derivative of 3x^3 + 2

User Dswatik
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Answer:


\displaystyle y' = 9x^2

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

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

Derivative Property [Addition/Subtraction]:
\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify


\displaystyle y = 3x^3 + 2

Step 2: Differentiate

  1. Derivative Property [Addition/Subtraction]:
    \displaystyle y' = (d)/(dx)[3x^3] + (d)/(dx)[2]
  2. Rewrite [Derivative Property - Multiplied Constant]:
    \displaystyle y' = 3 (d)/(dx)[x^3] + (d)/(dx)[2]
  3. Basic Power Rule:
    \displaystyle y' = 9x^2

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

Unit: Differentiation

User Aroon
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