Question

whats the derivative of (lnt)^2

Answer 1

Answer:

$\displaystyle \frac{dy}{dt} = \frac{2 \ln t}{t}$

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]:                                                                                 $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle y = (\ln t)^2$

Step 2: Differentiate

1. Basic Power Rule [Derivative Rule - Chain Rule]:                                       $\displaystyle y' = 2 \ln (t) \cdot \frac{d}{dt}[\ln t]$
2. Logarithmic Differentiation:                                                                         $\displaystyle y' = \frac{2 \ln t}{x}$

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

Unit: Differentiation