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:
23. x = 4; DE = 44
24. x = 25; DS = 28
Step-by-step explanation:
23. Point S is the midpoint of DE, so ...
DS = SE
3x +10 = 6x -2
12 = 3x . . . . . . . . . add 2-3x
4 = x . . . . . . . . . . . divide by 3
Then DS has length ...
DS = 3x +10 = 12 +10 = 22
and DE is twice that length, so ...
DE = 44
__
24. DS is half the length of DE, so is ...
DS = DE/2 = 56/2
DS = 28
Then x can be found from ...
DS = x +3
28 -3 = x = 25 . . . . . substitute value for DS
_____
<em>Comment on problem 24</em>
Sometimes it is easier to work parts of a problem out of sequence. Here, finding DS first makes finding x easier.
Answer(s):
Exact Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3
Mixed Number Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3 2 3
Improper Fraction Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 11 3
Decimal Form: x + 2 y − 3 z = 15 , 2 x − 2 z = 6 , 3. ¯ 6
Hope this helps, have a nice day/night! :D
Answer:
Step-by-step explanation:
The object is at or above 34.3 meters for six seconds.