Answer:
c= 7
Step-by-step explanation:
Answer:

Step-by-step explanation:
we know that
The formula to calculate the coordinates of the midpoint between two points is equal to

we have that
The coordinates of diagonal WY are

substitute in the formula to calculate the midpoint



Answer:
A because they can never be equal because each month Moira adds 5 dollars and Nathan adds 8 dollars
Distribute easy: 8x; 2/3 of 12 is 8.
8x-6
8x-6
Answer:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Algebra I</u>
- Factoring
- Exponential Rule [Dividing]:

- Exponential Rule [Powering]:

<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
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)
Quotient Rule: ![\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Trig Derivative: ![\displaystyle \frac{d}{dx}[cos(u)] = -u'sin(u)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%28u%29%5D%20%3D%20-u%27sin%28u%29)
eˣ Derivative: ![\displaystyle \frac{d}{dx}[e^u] = u'e^u](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5Eu%5D%20%3D%20u%27e%5Eu)
Step-by-step explanation:
<u>Step 1: Define</u>

<u>Step 2: Differentiate</u>
- [Derivative] Quotient Rule:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - \frac{d}{dx}[e^{2x}](3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%20%5Cfrac%7Bd%7D%7Bdx%7D%5Be%5E%7B2x%7D%5D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Numerator] eˣ derivative:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{(e^{2x})^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7B%28e%5E%7B2x%7D%29%5E2%7D)
- [Derivative] [Fraction - Denominator] Exponential Rule - Powering:
![\displaystyle y' = \frac{\frac{d}{dx}[(3x + 1)cos(2x)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7Bd%7D%7Bdx%7D%5B%283x%20%2B%201%29cos%282x%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Product Rule:
![\displaystyle y' = \frac{[\frac{d}{dx}[3x + 1]cos(2x) + \frac{d}{dx}[cos(2x)](3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%201%5Dcos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Basic Power Rule:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%281%20%5Ccdot%203x%5E%7B1%20-%201%7D%29cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] (Parenthesis) Simplify:
]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%282x%29%5D%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] [Brackets] Trig derivative:
![\displaystyle y' = \frac{[3cos(2x) -2sin(2x)(3x + 1)]e^{2x} - 2e^{2x}(3x + 1)cos(2x)}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B3cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%5De%5E%7B2x%7D%20-%202e%5E%7B2x%7D%283x%20%2B%201%29cos%282x%29%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{e^{2x}[(3cos(2x) -2sin(2x)(3x + 1)) - 2(3x + 1)cos(2x)]}{e^{4x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Be%5E%7B2x%7D%5B%283cos%282x%29%20-2sin%282x%29%283x%20%2B%201%29%29%20-%202%283x%20%2B%201%29cos%282x%29%5D%7D%7Be%5E%7B4x%7D%7D)
- [Derivative] [Fraction] Simplify [Exponential Rule - Dividing]:

- [Derivative] [Fraction - Numerator] Factor:
![\displaystyle y' = \frac{3cos(2x) -2(3x + 1)[sin(2x) + cos(2x)]}{e^{2x}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B3cos%282x%29%20-2%283x%20%2B%201%29%5Bsin%282x%29%20%2B%20cos%282x%29%5D%7D%7Be%5E%7B2x%7D%7D)
Topic: AP Calculus AB/BC
Unit: Derivatives
Book: College Calculus 10e