Answer:

General Formulas and Concepts:
<u>Algebra I</u>
Terms/Coefficients
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
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>
- Derivative Rule [Quotient Rule]:

- Basic Power Rule:

- Exponential Differentiation:

- Simplify:

- Rewrite:

- Factor:

Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
Answer:
(f-g)(x) = x^2 - 3x + 2
Step-by-step explanation:
If f(x) = x^2+ 1 and g(x) = 3x-1
Then (f-g)(x) = (x^2+ 1 )(-(3x-1)
(f-g)(x) = x^2 + 1 - 3x + 1
(f-g)(x) = x^2 - 3x + 2
Answer:
x<2
Step-by-step explanation:
I didnt feel like typing it out but the explanation is in the picture hope this helps :)
Answer:
The solution is (-2, 0)
Step-by-step explanation:
Re-write -2x=-y+4 x=-2 in column form:
x=-2
-2x=-y+4
Next, substitute -2 for x in the second equation:
-2(-2) = -y + 4, or:
4 = -y + 4. Thus, y must be 0.
The solution is (-2, 0)
Answer: 525 cycles per second.
Step-by-step explanation:
The equation for inverse variation between x and y is given by :-
(1)
Given : The length of a violin string varies inversely with the frequency of its vibrations.
A violin string 14 inches long vibrates at a frequency of 450 cycles per second.
Let x = length of a violin
y= frequency of its vibrations
To find: The frequency of a 12 inch violin string.
Put
in equation (1) , we get
Divide both sides by 12 , we get

Hence, the frequency of a 12 inch violin string = 525 cycles per second.