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Obtain the derivative of y=2x^2​

User Serra
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Answer:


\displaystyle y' = 4x

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 y = 2x^2

Step 2: Differentiate

  1. Derivative Property [Multiplied Constant]:
    \displaystyle y' = 2(x^2)'
  2. Basic Power Rule:
    \displaystyle y' = 4x

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

Unit: Differentiation

User MrPurpleStreak
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