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
I’m struggling too I’m sorry
For 11, we start by plugging 1 in, getting 2(1)^2+1-5=-2=y
Plugging 1+m instead, we get 2(1+m)^2+1+m-5=2(1+2m+m^2)+1+m-5
= 2+4m+2m^2+1+m-5= 2m^2+5m-2. We have to find the difference between that and -2, so 2m^2+5m-2 -(-2)=2m^2+5m
Differentiating 12, we use the Power Rule to get -6x^2+14, and plugging x=1 into it, we get -6(1)^2+14=-6+14=18
Answer:
17-2*3-8=3
Step-by-step explanation:
We have given:
17_2_3_8=3 insert + - × or ÷ symbols to make each statement true?
<u>Solution:</u>
We will insert multiplication sign between 2 and 3 and then subtract all the terms
<u>17-2*3-8=3</u>
We will solve it according to the DMAS rule:
DMAS rule is followed when multiple arithmetic operations are there in a given problem like addition, subtraction, multiplication and division. It tells they should be performed in order of Division, Multiplication, Addition and Subtraction. Without DMAS rule all mathematical equations will come up with different answers.
Lets solve the expression and check whether the L.H.S = R.H.S
17-2*3-8=3
17-6-8=3
11-8=3
3 =3
<em>Be sure to multiply first and then subtract</em>
⇒You can also insert addition sign in place of multiplication. It will give the same answer