Mathematics, 01.03.2021 07:20 mandyO1

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 =
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Let y = 5e5z

A. Find the differential dy
25e53
dy
B. Use part A. to find dy when x = - 3 and dir

Answers: 1

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Answers

Answer from: skyrileycasting

$\displaystyle dy = 25e^{5x}dx\\dy = 3.27 \cdot 10^7$

General Formulas and Concepts:

Math

RoundingEuler's Number e - 2.71828

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Calculus

Derivatives

Derivative Notation

Differentials

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

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

Step-by-step explanation:

Part A

Step 1: Define

$\displaystyle y = 5e^{5x}$

Step 2: Differentiate

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

Part B

Step 1: Define

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

[Given] x = 3, dx = 0.4

Step 2: Evaluate

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

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

Unit: Differentials

Book: College Calculus 10e

Answer from: Quest

step-by-step explanation:

Answer from: Quest

14.29%

step-by-step explanation:

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Let y = 5e5z A. Find the differential dy
25e53
dy
B. Use part A. to find dy when...