Answer:
![\displaystyle \frac{d}{dx}[3x + 5x] = 8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5B3x%20%2B%205x%5D%20%3D%208)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]: ![\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bcf%28x%29%5D%20%3D%20c%20%5Ccdot%20f%27%28x%29)
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
<u>Step 2: Differentiate</u>
- Simplify:
- Derivative Property [Multiplied Constant]:
![\displaystyle y' = 8\frac{d}{dx}[x]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%208%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5D)
- Basic Power Rule:
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
The geography of the Fertile Crescent affected the growth of Mesopotamian civilizations by soil being very fertile and great for farming and planting things, the Euphrates, Tigris, and Nile rivers were also great for farming but they where also trade routes.
Step-by-step explanation:
It is the graph shifted 6 units right
"h and k cannot both equal zero" -- yes, it can. if the vertex of a parabola is at (0, 0), there's nothing incorrect/invalid about that!!
"k and c have the same value" -- k and c do not have the same value. "k" is the y-value of the vertex and c is the constant in your quadratic equation, and the constant is not necessarily the y-value.
"the value of a remains the same" -- this is true. the a's in your equations are the same values, because the a-value is the coefficient of the x-variable in both equations. y = a(x - h)^2 and y = ax^2 -- both of these have a applying to your x-variables.
"h is equal to one half -b" -- this isn't true. the formula for calculating the x value of the vertex (h is the x-value of the vertex) is h = (-b/2a). -b/2a is not the same as one half -b because this answer choice doesn't involve the a-value.
