1. What is the article mostly about?

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

3 years ago

QUESTION 1 Which of the following statements is NOT true about smoking cigars and pipes? O There is an increased risk of develop

Gekata [30.6K]

Answer:

I think the answer would be c.

Explanation:

3 0

3 years ago

13. Type AB blood has often been called the universal recipient meaning a person with

notka56 [123]

Giving the person type a or type B or type O blood would introduce antibodies into the blood that the body wouldn't be able to control

4 0

3 years ago

Read 2 more answers

Write two scenarios in which you can imagine yourself or someone you know being pressured to engage in inappropriate sexual acti

ss7ja [257]

1) My friend and I were invited to a party by her new boyfriend. When we arrived, it was very noticeable that a lot of my peers were under the influence of alcohol. My friend started drinking, and drinking fast. By the time her boyfriend had found her, she was very well intoxicated. While she was under the influence, he asked her to do sexual things.
-My friend was susceptible to pressure because she was influenced by alcohol, which affects the decision making process and thoughts in general.

3 0

3 years ago

When many organ systems work together, they can form a(n):

spayn [35]

Answer:

D. Organism

Explanation:

8 0

3 years ago

Read 2 more answers