Respuesta :

Space

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{66}{x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 66 \ln x + 135[/tex]

Step 2: Differentiate

  1. Derivative Property [Addition/Subtraction]:                                                 [tex]\displaystyle y' = \frac{d}{dx}[66 \ln x] + \frac{d}{dx}[135][/tex]
  2. Derivative Property [Multiplied Constant]:                                                   [tex]\displaystyle y' = 66\frac{d}{dx}[\ln x] + \frac{d}{dx}[135][/tex]
  3. Logarithmic Differentiation:                                                                         [tex]\displaystyle y' = \frac{66}{x}[/tex]

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

Unit: Differentiation

Otras preguntas