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VikaD [51]
3 years ago
5

Please, someone, help very hard

Mathematics
1 answer:
Law Incorporation [45]3 years ago
3 0

Answer:

A. G'(5) = 20

B. G'(5) = -1

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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

<u>Algebra I</u>

  • Functions
  • Function Notation

<u>Calculus</u>

Derivatives

Derivative Notation

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

Derivative Rule [Quotient Rule]:                                                                             \displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}

Step-by-step explanation:

<u>Step 1: Define</u>

[Given] F(5) = 4, F'(5) = 4, H(5) = 2, H'(5) = 3

[Given] A. G(z) = F(z) · H(z)

[Given] B. G(w) = F(w) / H(w)

[Find] G'(5)

<u>Step 2: Differentiate</u>

A. G(z) = F(z) · H(z)

  1. [Derivative] Product Rule:                                                                              G'(z) = F'(z)H(z) + F(z)H'(z)

B. G(w) = F(w) / H(w)

  1. [Derivative] Quotient Rule:                                                                             G'(w) = [F'(w)H(w) - F(w)H'(w)] / H²(w)

<u>Step 3: Evaluate</u>

A. G'(5)

  1. Substitute in <em>x </em>[Function]:                                                                              G'(5) = F'(5)H(5) + F(5)H'(5)
  2. Substitute in function values:                                                                        G'(5) = 4(2) + 4(3)
  3. Multiply:                                                                                                           G'(5) = 8 + 12
  4. Add:                                                                                                                 G'(5) = 20

B. G'(5)

  1. Substitute in <em>x</em> [Function]:                                                                              G'(5) = [F'(5)H(5) - F(5)H'(5)] / H²(5)
  2. Substitute in function values:                                                                        G'(5) = [4(2) - 4(3)] / 2²
  3. Exponents:                                                                                                      G'(5) = [4(2) - 4(3)] / 4
  4. [Brackets] Multiply:                                                                                         G'(5) = [8 - 12] / 4
  5. [Brackets] Subtract:                                                                                        G'(5) = -4 / 4
  6. Divide:                                                                                                             G'(5) = -1

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

Unit: Derivatives

Book: College Calculus 10e

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