Respuesta :

Space

Answer:

[tex]\displaystyle h'(s) = 64s + 20[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Distributive Property

Algebra I

  • Terms/Coefficients

Calculus

Derivatives

Derivative Notation

Derivative of a constant is 0

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:                                                                                  [tex]\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle h(s) = (-8s - 9)(-4s + 2)[/tex]

Step 2: Differentiate

  1. [Derivative] Product Rule:                                                                               [tex]\displaystyle h'(s) = \frac{d}{ds}[(-8s - 9)](-4s + 2) + (-8s - 9)\frac{d}{ds}[(-4s + 2)][/tex]
  2. [Derivative] Basic Power Rule:                                                                       [tex]\displaystyle h'(s) = (1 \cdot -8s^{1 - 1} - 0)(-4s + 2) + (-8s - 9)(1 \cdot -4s^{1 - 1} - 0)[/tex]
  3. [Derivative] Simplify:                                                                                         [tex]\displaystyle h'(s) = (-8)(-4s + 2) + (-8s - 9)(-4)[/tex]
  4. [Derivative] Distribute [Distributive Property]:                                              [tex]\displaystyle h'(s) = 32s - 16 + 32s + 36[/tex]
  5. [Derivative] Combine like terms:                                                                     [tex]\displaystyle h'(s) = 64s + 20[/tex]

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

Unit: Derivatives

Book: College Calculus 10e

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