Respuesta :

Space

Answer:

[tex]\displaystyle \frac{dy}{dx} = \frac{-4}{3x^5}[/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]

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = \frac{\frac{1}{x^4}}{3}[/tex]

Step 2: Differentiate

  1. Derivative Property [Addition/Subtraction]:                                                 [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx} \bigg[ \frac{1}{x^4} \bigg][/tex]
  2. Rewrite:                                                                                                         [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx}[x^{-4}][/tex]
  3. Basic Power Rule:                                                                                         [tex]\displaystyle y' = \frac{1}{3}(-4x^{-5})[/tex]
  4. Simplify:                                                                                                         [tex]\displaystyle y' = \frac{-4}{3x^5}[/tex]

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

Unit: Differentiation

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