Answer:
\(\displaystyle y' = \frac{1}{x \ln(x)}\)
General Formulas and Concepts:
Calculus
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Derivative Rule [Chain Rule]: \(\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)\)
Step-by-step explanation:
Step 1: Define
Identify
\(\displaystyle y = \ln \Big( \ln(x) \Big)\)
Step 2: Differentiate
- Logarithmic Differentiation [Derivative Rule - Chain Rule]: \(\displaystyle y' = \frac{1}{\ln(x)} \cdot \frac{d}{dx}[\ln(x)]\)
- Logarithmic Differentiation: \(\displaystyle y' = \frac{1}{\ln(x)} \cdot \frac{1}{x}\)
- Simplify: \(\displaystyle y' = \frac{1}{x \ln(x)}\)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
