Respuesta :

Space

Answer:

[tex]\displaystyle \frac{dy}{dx} = 20x^3[/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]  

Basic Power Rule:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle y = 5x^4 + 4[/tex]

Step 2: Differentiate

  1. Derivative Property [Addition/Subtraction]:                                                 [tex]\displaystyle y' = \frac{d}{dx}[5x^4] + \frac{d}{dx}[4][/tex]
  2. Rewrite [Derivative Property - Multiplied Constant]:                                   [tex]\displaystyle y' = 5\frac{d}{dx}[x^4] + \frac{d}{dx}[4][/tex]
  3. Basic Power Rule:                                                                                         [tex]\displaystyle y' = 20x^3[/tex]

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

Unit: Differentiation

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