Answer :

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Answer:

[tex]\displaystyle \frac{d}{dx}[e^\big{2x}] = 2e^\big{2x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

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

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = e^\big{2x}[/tex]

Step 2: Differentiate

  1. Exponential Differentiation [Derivative Rule - Chain Rule]:                       [tex]\displaystyle \frac{d}{dx} = e^\big{2x} \cdot \frac{d}{dx}[2x][/tex]
  2. Basic Power Rule [Derivative Property - Multiplied Constant]:                 [tex]\displaystyle \frac{d}{dx} = e^\big{2x} \cdot 2[/tex]
  3. Simplify:                                                                                                         [tex]\displaystyle \frac{d}{dx} = 2e^\big{2x}[/tex]

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

Unit: Differentiation

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