Answered

Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Let y = 5e5z
A. Find the differential dy
25e53
dy
B. Use part A. to find dy when x = - 3 and dir = 0.4.
Round your answer to 2 decimal(s).
dy =
Submit Question

Let Y 5e5z A Find The Differential Dy 25e53 Dy B Use Part A To Find Dy When X 3 And Dir 04 Round Your Answer To 2 Decimals Dy Submit Question class=

Sagot :

Space

Answer:

[tex]\displaystyle dy = 25e^{5x}dx\\dy = 3.27 \cdot 10^7[/tex]

General Formulas and Concepts:

Math

  • Rounding
  • Euler's Number e - 2.71828

Pre-Algebra

Order of Operations: BPEMDAS

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

Calculus

Derivatives

Derivative Notation

Differentials

Basic Power Rule:

  • f(x) = cxⁿ
  • f’(x) = c·nxⁿ⁻¹

eˣ Derivative: [tex]\displaystyle \frac{dy}{dx}[e^u] = u'e^u[/tex]

Step-by-step explanation:

Part A

Step 1: Define

[tex]\displaystyle y = 5e^{5x}[/tex]

Step 2: Differentiate

  1. [Function] eˣ Derivative:                                                                                 [tex]\displaystyle \frac{dy}{dx} = \frac{dy}{dx}[5x] \cdot 5e^{5x}[/tex]
  2. [Derivative] Basic Power Rule:                                                                      [tex]\displaystyle \frac{dy}{dx} = 5x^{1 - 1} \cdot 5e^{5x}[/tex]
  3. [Derivative] Simplify:                                                                                       [tex]\displaystyle \frac{dy}{dx} = 5 \cdot 5e^{5x}[/tex]
  4. [Derivative] Multiply:                                                                                       [tex]\displaystyle \frac{dy}{dx} = 25e^{5x}[/tex]
  5. [Derivative] [Multiplication Property of Equality] Isolate dy:                        [tex]\displaystyle dy = 25e^{5x}dx[/tex]

Part B

Step 1: Define

[Differential] [tex]\displaystyle dy = 25e^{5x}dx[/tex]

[Given] x = 3, dx = 0.4

Step 2: Evaluate

  1. Substitute in variables [Differential]:                                                             [tex]\displaystyle dy = 25e^{5(3)}(0.4)[/tex]
  2. [Differential] [Exponents] Multiply:                                                                [tex]\displaystyle dy = 25e^{15}(0.4)[/tex]
  3. [Differential] Evaluate exponents:                                                                 [tex]\displaystyle dy = 25(3.26902 \cdot 10^6)(0.4)[/tex]
  4. [Differential] Multiply:                                                                                     [tex]\displaystyle dy = (8.17254 \cdot 10^7)(0.4)[/tex]
  5. [Differential] Multiply:                                                                                     [tex]\displaystyle dy = 3.26902 \cdot 10^7[/tex]
  6. [Differential] Round:                                                                                       [tex]\displaystyle dy = 3.27 \cdot 10^7[/tex]

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

Unit: Differentials

Book: College Calculus 10e

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you chose Westonci.ca. Revisit us for updated answers from our knowledgeable team.