What temperature kills germs in the house?

Differentiate the following functions (i) x(1+x)^3

statuscvo [17]

Answer:

$\displaystyle y' = (1 + x)^2(4x + 1)$

General Formulas and Concepts:

Algebra I

Terms/Coefficients
Functions
Function Notation
Factoring

Calculus

Derivatives

Derivative Notation

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) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]: $\displaystyle \frac{d}{dx} [f(x)g(x)]=f'(x)g(x) + g'(x)f(x)$

Derivative Rule [Chain Rule]: $\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)$

Explanation:

Step 1: Define

Identify

y = x(1 + x)³

Step 2: Differentiate

Product Rule [Derivative Rule - Chain Rule]: $\displaystyle y' = \frac{d}{dx}[x] \cdot (1 + x)^3 + x \cdot \frac{d}{dx}[(1 + x)^3] \cdot \frac{d}{dx}[1 + x]$
Derivative Property [Addition/Subtraction]: $\displaystyle y' = \frac{d}{dx}[x] \cdot (1 + x)^3 + x \cdot \frac{d}{dx}[(1 + x)^3] \cdot (\frac{d}{dx}[1] + \frac{d}{dx}[x])$
Basic Power Rule: $\displaystyle y' = x^{1 - 1} \cdot (1 + x)^3 + x \cdot 3(1 + x)^{3 - 1} \cdot (0 + x^{1 - 1})$
Simplify: $\displaystyle y' = (1 + x)^3 + 3x(1 + x)^2$
Factor: $\displaystyle y' = (1 + x)^2 \bigg[ (1 + x) + 3x \bigg]$
Combine like terms: $\displaystyle y' = (1 + x)^2(4x + 1)$

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

Unit: Derivatives

Book: College Calculus 10e

5 0

2 years ago

_____ and _____ are often the 2 most important reasons specific foods are consumed in north america.

Nonamiya [84]

The Taste and Texture are often the two most important reasons specific foods are consumed in North America.

The taste matters as it is the most important factor that determines food selection or preference. Its a type of pleasure people experiences when eating a particular food.

The appearance and texture of food is the second major factor. These sensory aspects are thought to influence, in particular or specific food choice.

The factors such as- taste, odor, appearance, texture, temperature, sound, and trigeminal nerve which together constitute flavor are sensory features of a food which people use to assess palatability. The Palatability is the hedonic evaluation of odor-sensory food cues under standardized conditions.

To learn more about trigeminal nerve here

brainly.com/question/13055387

#SPJ4

4 0

1 year ago

Terrance wants to purchase a supplement that claims it is all-natural and will help him lose 15 pounds in two weeks. His friend

KIM [24]

Answer:

1. to good to be true(like this one)

2. don't bandwagon even if you see other people useing does not mean it works

3. even if your fravoirite you tuber is using it this does not mean it works either it just means their getting paid

Hope This Helps!!!

8 0

1 year ago

What is the difference between carcinoma and sarcoma in regard to the types of tissue where they are found?

Annette [7]

Answer: A carcinoma forms in the skin or tissue cells that line the body's internal organs, such as the kidneys and liver. A sarcoma grows in the body's connective tissue cells, which include fat, blood vessels, nerves, bones, muscles, deep skin tissues and cartilage.

Explanation:

6 0

2 years ago

Where should household cleaners be stored?

butalik [34]

Answer:

A

Explanation:

5 0

2 years ago