Answer:
C. ![\displaystyle \frac{cos(x)}{x} - ln(x)sin(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7Bcos%28x%29%7D%7Bx%7D%20-%20ln%28x%29sin%28x%29)
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
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)
Trig Derivatives
Logarithmic Derivatives
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
![\displaystyle f(x) = ln(x)cos(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20ln%28x%29cos%28x%29)
<u>Step 2: Differentiate</u>
- Derivative Rule [Product Rule]:
![\displaystyle f'(x) = \frac{d}{dx}[ln(x)]cos(x) + ln(x)\frac{d}{dx}[cos(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%5Bln%28x%29%5Dcos%28x%29%20%2B%20ln%28x%29%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%28x%29%5D)
- Logarithmic Derivative:
![\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)\frac{d}{dx}[cos(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%7Dcos%28x%29%20%2B%20ln%28x%29%5Cfrac%7Bd%7D%7Bdx%7D%5Bcos%28x%29%5D)
- Trig Derivative:
![\displaystyle f'(x) = \frac{1}{x}cos(x) + ln(x)[-sin(x)]](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7B1%7D%7Bx%7Dcos%28x%29%20%2B%20ln%28x%29%5B-sin%28x%29%5D)
- Simplify:
![\displaystyle f'(x) = \frac{cos(x)}{x} - ln(x)sin(x)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%27%28x%29%20%3D%20%5Cfrac%7Bcos%28x%29%7D%7Bx%7D%20-%20ln%28x%29sin%28x%29)
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Book: College Calculus 10e
Answer:
(x+4)(x-5)
Step-by-step explanation:
You need to find two numbers that multiply to be -20 but add up to be -1.
Answer: I have no clue what the second one is but the first one is 1.
Step-by-step explanation:
Answer: 987,654,314,000
Step-by-step explanation:
Answer:
5.401×10^-1
Step-by-step explanation:
You move the decimal over one to get5.401×10^−1