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
180 degree
Step-by-step explanation:
supplementary means anhke havinv sum of 180 degree
so sum to two supplemrntary angles is 180 drgree
Answer:
5 + 2 = 7.
Step-by-step explanation:
If you mean the other way around then no.
2 + 7 doesn't equal 5.
14 units^2 because you divide the shape into two parts find the area of each shape then add it together