Which of these are designer drugs? Check all that apply.

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

A patient asked a physical therapist to e-mail him some information on what other patients that he has

Sveta_85 [38]

Answer:rather than email,the therapist should explain about the procedure face to face

Explanation:

so that the patient will understand about the procedure and he/she will not be scared to proceed with the procedure

6 0

3 years ago

Which of these is overconsumed in the united states

g100num [7]

Hello! The U.S. has one of the highest obesity rates in the world. Americans don't consume enough leafy greens, Vitamin C, and sweet potatoes. Those foods are healthy, but overly processed goods and sweets are consumed a lot, which explains why America's obesity rate is so high. In fact, 1 in 3 adults are obese and 1 in 6 children are obese. Lack of exercise also contributes to obesity as the sweets are turned into fat and it's stored there.The answer is A.

6 0

3 years ago

What comprises a team in basketball? How many players and what positions?

loris [4]

In basketball, there are ten players on the court, which isn’t including refs. five players from each team play at a time. the most basic positions in basketball is point guard and post. point guards do a lot of ball handling and outside shooting. posts stay within or near the lane, and they can shoot outside the lane. usually, but not always, posts are stronger and taller. hope it helps <3

5 0

3 years ago

Use apples, sweet cherries, oranges, grapefruit, or pumpkins in an example that demonstrates interdependence and the role that h

Free_Kalibri [48]

Answer:

The correct answer is - they are interdependent for pollinating crops and fruit plants and get nectar for their survival.

Explanation:

Honey bees play an important role in agriculture as these organisms help in pollinating crops, plants, busher, and trees and transfer pollen. from one plant or tree to another for their fertilization and fruit and flower production. Honey bees not just collect pollen but nectar which is essential for their own survival.

These bees pollinate apples, sweet cherries, grapefruit, oranges, and pumpkins as they take pollen from the flower of one plant with the nectar and leaves on the other flower of another plant. Most plants including cherries and almonds depend on honey bees dominantly for pollination and can be extinct in absence of the bees.

7 0

2 years ago