Answer:
(i) 
(ii) 
(iii) ![\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Be%5Ex%5Bxln%282x%29%20%2B%201%5D%7D%7Bx%7D)
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)
Derivative Property [Addition/Subtraction]:
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 [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)
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)
Exponential Differentiation
Logarithmic Differentiation
Step-by-step explanation:
(i)
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Product Rule:
![\displaystyle y' = (3x^2 - x)'ln(2x + 1) + (3x^2 - x)[ln(2x + 1)]'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%283x%5E2%20-%20x%29%27ln%282x%20%2B%201%29%20%2B%20%283x%5E2%20-%20x%29%5Bln%282x%20%2B%201%29%5D%27)
- Basic Power Rule/Logarithmic Differentiation [Chain Rule]:

- Basic Power Rule:

- Simplify [Factor]:

(ii)
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Quotient Rule:

- Basic Power Rule/Logarithmic Differentiation:

- Rewrite:

- Simplify:

(iii)
<u>Step 1: Define</u>
<em>Identify</em>

<u>Step 2: Differentiate</u>
- Product Rule:
![\displaystyle y' = (e^x)'ln(2x) + e^x[ln(2x)]'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%28e%5Ex%29%27ln%282x%29%20%2B%20e%5Ex%5Bln%282x%29%5D%27)
- Exponential Differentiation/Logarithmic Differentiation [Chain Rule]:

- Basic Power Rule:

- Simplify:

- Rewrite:

- Factor:
![\displaystyle y' = \frac{e^x[xln(2x) + 1]}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7Be%5Ex%5Bxln%282x%29%20%2B%201%5D%7D%7Bx%7D)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
<span>5x^2 = 45</span>
Divide each side by 5 :
x^2 = 9
Take the square root of each side:
x = +3 or -3 .
Did I go too fast for you ?
Using the normal distribution, it is found that approximately 40% of the scores are greater than 413.
<h3>Normal Probability Distribution</h3>
The z-score of a measure X of a normally distributed variable with mean
and standard deviation
is given by:

- The z-score measures how many standard deviations the measure is above or below the mean.
- Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.
In this problem, we have that the mean and the standard deviation of the scores are given by:

Approximately 40% of the scores are greater than the 60th percentile, which is <u>X when Z = 0.253</u>.
Then:


X - 400 = 50(0.253)
X = 412.65.
Rounding up, approximately 40% of the scores are greater than 413.
More can be learned about the normal distribution at brainly.com/question/24663213
#SPJ1
Answer:
2/13
Step-by-step explanation:
There are thirteen shapes and out of that two are
Answer:
please tell me if im wrong!
Step-by-step explanation:
answer: 16 √ 3