Answer:
![\displaystyle y' = \frac{-2}{x \ln (10)[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B-2%7D%7Bx%20%5Cln%20%2810%29%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Derivative Property [Addition/Subtraction]: ![\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%20%2B%20g%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%5D%20%2B%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bg%28x%29%5D)
Derivative Rule [Basic Power Rule]:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
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)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify.</em>

<u>Step 2: Differentiate</u>
- [Function] Derivative Rule [Quotient Rule]:
![\displaystyle y' = \frac{[\log (x) - 2][\log (x)]' - [\log (x) - 2]'[\log (x)]}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Clog%20%28x%29%20-%202%5D%5B%5Clog%20%28x%29%5D%27%20-%20%5B%5Clog%20%28x%29%20-%202%5D%27%5B%5Clog%20%28x%29%5D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Rewrite [Derivative Rule - Addition/Subtraction]:
![\displaystyle y' = \frac{[\log (x) - 2][\log (x)]' - [\log (x)' - 2'][\log (x)]}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Clog%20%28x%29%20-%202%5D%5B%5Clog%20%28x%29%5D%27%20-%20%5B%5Clog%20%28x%29%27%20-%202%27%5D%5B%5Clog%20%28x%29%5D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Logarithmic Differentiation:
![\displaystyle y' = \frac{[\log (x) - 2]\frac{1}{\ln (10)x} - [\frac{1}{\ln (10)x} - 2'][\log (x)]}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Clog%20%28x%29%20-%202%5D%5Cfrac%7B1%7D%7B%5Cln%20%2810%29x%7D%20-%20%5B%5Cfrac%7B1%7D%7B%5Cln%20%2810%29x%7D%20-%202%27%5D%5B%5Clog%20%28x%29%5D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Derivative Rule [Basic Power Rule]:
![\displaystyle y' = \frac{[\log (x) - 2]\frac{1}{\ln (10)x} - \frac{1}{\ln (10)x}[\log (x)]}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5B%5Clog%20%28x%29%20-%202%5D%5Cfrac%7B1%7D%7B%5Cln%20%2810%29x%7D%20-%20%5Cfrac%7B1%7D%7B%5Cln%20%2810%29x%7D%5B%5Clog%20%28x%29%5D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Simplify:
![\displaystyle y' = \frac{\frac{\log (x) - 2}{\ln (10)x} - \frac{\log (x)}{\ln (10)x}}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7B%5Clog%20%28x%29%20-%202%7D%7B%5Cln%20%2810%29x%7D%20-%20%5Cfrac%7B%5Clog%20%28x%29%7D%7B%5Cln%20%2810%29x%7D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Simplify:
![\displaystyle y' = \frac{\frac{-2}{\ln (10)x}}{[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B%5Cfrac%7B-2%7D%7B%5Cln%20%2810%29x%7D%7D%7B%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
- Rewrite:
![\displaystyle y' = \frac{-2}{x \ln (10)[\log (x) - 2]^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20y%27%20%3D%20%5Cfrac%7B-2%7D%7Bx%20%5Cln%20%2810%29%5B%5Clog%20%28x%29%20-%202%5D%5E2%7D)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
Measurement error.
Step-by-step explanation:
Measurement Error are the error when there is difference found in true value of data and measured quantity of data. This difference could be found if we are missing some data in the sample.
The error could be reduced by carefully designing the process of data collection and it´s measurement.
Measurement error are classified into two type of error:
- Random error.
- Systematic error.
The answer would most likely be 1 19/30
Answer:
42 in binary number is 101010.