Answer:

General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
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)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- [Function] Derivative Rule [Product Rule]:
![\displaystyle f'(x) = \frac{d}{dx}[9x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B9x%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Rewrite [Derivative Property - Multiplied Constant]:
![\displaystyle f'(x) = 9 \frac{d}{dx}[x^{10}] \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%209%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bx%5E%7B10%7D%5D%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Basic Power Rule:
![\displaystyle f'(x) = 90x^9 \tan^{-1}(x) + 9x^{10} \frac{d}{dx}[\tan^{-1}(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%2090x%5E9%20%5Ctan%5E%7B-1%7D%28x%29%20%2B%209x%5E%7B10%7D%20%5Cfrac%7Bd%7D%7Bdx%7D%5B%5Ctan%5E%7B-1%7D%28x%29%5D)
- Arctrig Derivative:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer: 4
<u>Step-by-step explanation:</u>
f(x) = 4x³ - x² + 1 g(x) = x - 1
g(2) = (2) - 1
= 1
f(1) = 4(1)³ - (1)² + 1
= 4 - 1 + 1
<h2> = 4</h2>
1) 4.28
2) 14.05
3) 2 r 30
4) $22.65
5) 684
6) 124.05
~this was rlly hard~
Answer:
y = -1/2x - 1
Step-by-step explanation:
Given equation:
y = 2x - 3
Given point: (x1,y1) = (-8,3)
This is in the form of y = mx + c,
so, m1 = 2
If the lines are perpendicular then the product of their slope will be - 1 i.e.
m1 x m2 = -1
2 x m2 = -1
m2 = -1/2
Now, using one point form formula,
y - y1 = m(x - x1)
or, y - 3 = -1/2( x - (-8))
or, y-3 = -1/2(x + 8)
or, y = -1/2x - 4 + 3
or, y = -1/2x - 1
This is the required equation.
3+2 = 5
80/5 =16
16 x 3 = 48
16 x 2 = 32
Answer= 48:32
I think this is right