History, 12.11.2020 15:40 hannahdrees0731

Differentiate the following
4x²(x³ - 5x) - 7x²?

Answers: 3

Show answers

Answers

Answer from: teamroper35

$\displaystyle \frac{dy}{dx} = 2x(10x^3 - 30x - 7)$

General Formulas and Concepts:

Algebra I

Terms/CoefficientsFactoring/Expanding

Calculus

Differentiation

DerivativesDerivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]$

Basic Power Rule:

f(x) = cxⁿf’(x) = c·nxⁿ⁻¹

Explanation:

Step 1: Define

Identify

$\displaystyle 4x^2(x^3 - 5x) - 7x^2$

Step 2: Differentiate

Expand: $\displaystyle 4x^5 - 20x^3 - 7x^2$ Derivative Property [Addition/Subtraction]: $\displaystyle \frac{dy}{dx} = \frac{d}{dx}[4x^5] - \frac{d}{dx}[20x^3] - \frac{d}{dx}[7x^2]$ Derivative Property [Multiplied Constant]: $\displaystyle \frac{dy}{dx} = 4\frac{d}{dx}[x^5] - 20\frac{d}{dx}[x^3] - 7\frac{d}{dx}[x^2]$ Basic Power Rule: $\displaystyle \frac{dy}{dx} = 4(5x^4) - 20(3x^2) - 7(2x)$ Simplify: $\displaystyle \frac{dy}{dx} = 20x^4 - 60x^2 - 14x$ Factor: $\displaystyle \frac{dy}{dx} = 2x(10x^3 - 30x - 7)$

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

Unit: Differentiation

Book: College Calculus 10e

Answer from: Quest

in 1803 the louisiana purchase took place, doubling the size of the country. by 1840 almost 7 million americans had migrated westward in hopes of securing land and being prosperous. the belief that settlers were destined to expand to the west is often referred to as manifest destiny.

explanation:

Answer from: Quest

the section of the chart that represents a point at which a bill needs approval from a majority of people in both chambers to advance is j, as this is the only section before the bill becomes law which has both rows (symbolizing the chambers) converging into one, meaning that the two parts of the congress have to approve of it before it can march on with the process.

Another question on History

History, 21.06.2019 23:30

The middle east is the best association with which international traded product

Answers: 1

Answer

History, 22.06.2019 06:30

Ineed a example for this test plz reflect on your decisions in the cases of hazelwood v. kuhlmeier and t.m. v. state of florida using the following questions: did your opinion reflect the majority or minority opinion on each case? did you tend to favor loose or strict interpretation of the laws and rights for each case? what factors most influenced your decision and interpretations in each cas

Answers: 2

Answer

History, 22.06.2019 15:00

Enter the word you received when you completed time line: french revolution,part1.

Answers: 3

Answer

History, 22.06.2019 15:30

Which of the following elements of american society did the beat generation moat strongly criticize? a. its promotion of consumerism. b. its tolerance of rock and roll. c. its focus on rural american values. d. its acceptance of individualism.