Question

Whats the derivative of (lnt)^2

Answer 1

`\displaystyle (dy)/(dt) = (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 (d)/(dx)[f(g(x))] =f'(g(x)) \cdot g'(x)`

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 (d)/(dt)[\ln t]`
2. Logarithmic Differentiation:
   `\displaystyle y' = (2 \ln t)/(x)`

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

Unit: Differentiation