Respuesta :

Space

Answer:

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

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Calculus

Derivatives

Derivative Notation

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

eˣ Derivative: [tex]\displaystyle \frac{d}{dx} [e^u]=e^u \cdot u'[/tex]

Step-by-step explanation:

Step 1: Define

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

Step 2: Differentiate

  1. [Derivative] eˣ Derivative [Chain Rule]:                                                       [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2x^{1 - 1} \cdot e^{2x}[/tex]
  2. [Derivative] Simplify:                                                                                     [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2x^{0} \cdot e^{2x}[/tex]
  3. [Derivative] Simplify:                                                                                     [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2(1) \cdot e^{2x}[/tex]
  4. [Derivative] Multiply:                                                                                     [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2 \cdot e^{2x}[/tex]
  5. [Derivative] Multiply:                                                                                     [tex]\displaystyle \frac{d}{dx}[e^{2x}] = 2e^{2x}[/tex]

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

Unit: Derivatives

Book: College Calculus 10e

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