Answer:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%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>
Exponential Properties
- Exponential Property [Rewrite]:

- Exponential Property [Root Rewrite]:
![\displaystyle \sqrt[n]{x} = x^{\frac{1}{n}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csqrt%5Bn%5D%7Bx%7D%20%3D%20x%5E%7B%5Cfrac%7B1%7D%7Bn%7D%7D)
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Multiplied Constant]:
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D)
<u>Step 2: Differentiate</u>
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \bigg( \frac{1}{2\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B2%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Derivative Property - Multiplied Constant]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{\sqrt{x}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7B%5Csqrt%7Bx%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Root Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{1}{x^\Big{\frac{1}{2}}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B1%7D%7Bx%5E%5CBig%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D%20%5Cbigg%29%27)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( x^\bigg{\frac{-1}{2}} \bigg)'](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20x%5E%5Cbigg%7B%5Cfrac%7B-1%7D%7B2%7D%7D%20%5Cbigg%29%27)
- Derivative Rule [Basic Power Rule]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{1}{2} \bigg( \frac{-1}{2} x^\bigg{\frac{-3}{2}} \bigg)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Cbigg%28%20%5Cfrac%7B-1%7D%7B2%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D%20%5Cbigg%29)
- Simplify:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4} x^\bigg{\frac{-3}{2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4%7D%20x%5E%5Cbigg%7B%5Cfrac%7B-3%7D%7B2%7D%7D)
- Rewrite [Exponential Rule - Rewrite]:
![\displaystyle \frac{d}{dx} \bigg[ \frac{1}{\sqrt{4x}} \bigg] = \frac{-1}{4x^\bigg{\frac{3}{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Cbigg%5B%20%5Cfrac%7B1%7D%7B%5Csqrt%7B4x%7D%7D%20%5Cbigg%5D%20%3D%20%5Cfrac%7B-1%7D%7B4x%5E%5Cbigg%7B%5Cfrac%7B3%7D%7B2%7D%7D%7D)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Round 57.8 to 60 and round 81 to 80.
60/80 or, if you simplify it, 3/4
And it is common knowledge that 3/4 = .75
So the quotient of 57.8/81 is ~.75
If i remember correctly i think you just cross multiply <span />
Answer:
<h2>This value is called the common difference</h2>
Step-by-step explanation:
The common difference is the constant value which is repeatedly added to each term in an arithmetic sequence to obtain the next term, it is basically the difference between consecutive numbers
To find the common difference we can subtract the previous term from the first time or the second to the last term from the last term, the idea of finding the common difference is basically subtracting the previous term form the subsequent term.
The answer is 10 hope this helps