Answer:
\(\displaystyle \frac{dy}{dt} = \frac{2 \ln t}{t}\)
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
\(\displaystyle y = (\ln t)^2\)
Step 2: Differentiate
- Basic Power Rule [Derivative Rule - Chain Rule]: \(\displaystyle y' = 2 \ln (t) \cdot \frac{d}{dt}[\ln t]\)
- Logarithmic Differentiation: \(\displaystyle y' = \frac{2 \ln t}{x}\)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
