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

v: l•w•h÷2.

v: 20•6•8 ÷2

v: 960÷2

v: 480

Answer from: Quest

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.

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

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