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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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:

Step-by-step explanation:

Part A

Step 1: Define

Step 2: Differentiate

[Function] eˣ Derivative:                                                                                 [Derivative] Basic Power Rule:                                                                      [Derivative] Simplify:                                                                                       [Derivative] Multiply:                                                                                       [Derivative] [Multiplication Property of Equality] Isolate dy:                        

Part B

Step 1: Define

[Differential]

[Given] x = 3, dx = 0.4

Step 2: Evaluate

Substitute in variables [Differential]:                                                             [Differential] [Exponents] Multiply:                                                                [Differential] Evaluate exponents:                                                                 [Differential] Multiply:                                                                                     [Differential] Multiply:                                                                                     [Differential] Round:                                                                                      

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

Unit: Differentials

Book: College Calculus 10e

MATÍAS: Antonio, ¿dónde está mi pluma?

ANTONIO: Tu pluma está al lado del libro de biología.

MATÍAS: ¿Y dónde está el libro de biología?

ANTONIO: Está en tu mochila.

MATÍAS: ¿Y mi mochila dónde está?

ANTONIO: Está cerca de la papelera, entre la puerta y la mesa.

MATÍAS: ¡Pero allí está la silla!

ANTONIO: Sí, y tu mochila está debajo de la silla.

TRANSLATION:

MATÍAS: Antonio, where is my pen?

ANTONIO: Your pen is next to the biology book.

MATÍAS: But where is the biology book?

ANTONIO: It's in your backpack.

MATÍAS: But where is my backpack?

ANTONIO: It's near the paper bin, between the door and the table.

MATÍAS: But there is the chair!

ANTONIO: Ok! but your backpack is under the chair.