Answer:

General Formulas and Concepts:
<u>Algebra I</u>
- Terms/Coefficients
- Functions
- Function Notation
- Factoring
<u>Calculus</u>
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)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
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)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29g%28x%29%5D%3Df%27%28x%29g%28x%29%20%2B%20g%27%28x%29f%28x%29)
Derivative Rule [Chain Rule]: ![\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28g%28x%29%29%5D%20%3Df%27%28g%28x%29%29%20%5Ccdot%20g%27%28x%29)
Explanation:
<u>Step 1: Define</u>
<em>Identify</em>
y = x(1 + x)³
<u>Step 2: Differentiate</u>
- 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]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D%20%5Ccdot%20%281%20%2B%20x%29%5E3%20%2B%20x%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%281%20%2B%20x%29%5E3%5D%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B1%20%2B%20x%5D)
- 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])](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D%20%5Ccdot%20%281%20%2B%20x%29%5E3%20%2B%20x%20%5Ccdot%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%281%20%2B%20x%29%5E3%5D%20%5Ccdot%20%28%5Cfrac%7Bd%7D%7Bdx%7D%5B1%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D%29)
- Basic Power Rule:

- Simplify:

- Factor:
![\displaystyle y' = (1 + x)^2 \bigg[ (1 + x) + 3x \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%281%20%2B%20x%29%5E2%20%5Cbigg%5B%20%281%20%2B%20x%29%20%2B%203x%20%5Cbigg%5D)
- Combine like terms:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Derivatives
Book: College Calculus 10e
Answer:
produce sound when they come together and then vibrate as air passes through them during exhalation of air from the lungs. This vibration produces the sound wave for your voice. In order for the sound to be clear and not raspy or hoarse, the vocal folds must vibrate together symmetrically and regularly
Explanation:
I would say minor changes.
brainiest is appreciated!
A. true. Because it allows you to see the reward of you doing the plan
Answer:
somatic ; peripheral
Explanation:
The somatic nervous system is part of the peripheral nervous system and is responsible for transmitting sensitive information and sending motor control information to skeletal muscles.
It is the main management system of voluntary movements and nerve center of dozens of sensory and motor nerves that enter and leave the central nervous system, in connection with the skin, organs and muscles of the body.
The somatic nervous system is part of a larger whole, the nervous system, guarantor of the control and management of the vast majority of the vital functions of our body, capturing the stimuli of the environment and those of the body itself to transmit, process information and generate effective answers based on what each situation requires.
The peripheral nervous system can be divided, from a functional point of view, into two parts: the autonomic nervous system, which is composed of sensory and motor fibers that connect the central nervous system (CNS) with the visceral organs, the smooth muscles and the secretory glands; and the somatic nervous system, which regulates the voluntary functions of the organism