Respuesta :

Space

Answer:

(B) 15

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

Algebra I

  • Functions
  • Function Notation

Calculus

Derivatives

Derivative Notation

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

Step-by-step explanation:

Step 1: Define

h(x) = f(g(x))

h'(1) = ?

Step 2: Differentiate

  1. Chain Rule:                                                                                                        h'(x) = f'(g(x)) · g'(x)

Step 3: Evaluate

  1. Substitute in x [Derivative]:                                                                              h'(1) = f'(g(1)) · g'(1)
  2. [Values] Substitute in function values:                                                            h'(1) = f'(3) · -3
  3. [Values] Substitute in derivative function values:                                          h'(1) = -5 · -3
  4. Multiply:                                                                                                             h'(1) = 15

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

Unit: Derivatives

Book: College Calculus 10e

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