Respuesta :

Space

Answer:

[tex]\displaystyle y' = \frac{1}{x \ln(x)}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

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 = \ln \Big( \ln(x) \Big)[/tex]

Step 2: Differentiate

  1. Logarithmic Differentiation [Derivative Rule - Chain Rule]:                       [tex]\displaystyle y' = \frac{1}{\ln(x)} \cdot \frac{d}{dx}[\ln(x)][/tex]
  2. Logarithmic Differentiation:                                                                         [tex]\displaystyle y' = \frac{1}{\ln(x)} \cdot \frac{1}{x}[/tex]
  3. Simplify:                                                                                                         [tex]\displaystyle y' = \frac{1}{x \ln(x)}[/tex]

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

Unit: Differentiation

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