Answer:
![\frac{d}{dx}[f(x)+g(x)+h(x)] = \frac{9\cdot x^{8}}{\sqrt{1-x^{18}}} - 81\cdot x^{80}-2\cdot x](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%5Bf%28x%29%2Bg%28x%29%2Bh%28x%29%5D%20%3D%20%5Cfrac%7B9%5Ccdot%20x%5E%7B8%7D%7D%7B%5Csqrt%7B1-x%5E%7B18%7D%7D%7D%20-%2081%5Ccdot%20x%5E%7B80%7D-2%5Ccdot%20x)
Step-by-step explanation:
This derivative consist in the sum of three functions: 
, 
and 
. According to differentiation rules, the derivative of a sum of functions is the same as the sum of the derivatives of each function. That is:
![\frac{d}{dx} [f(x)+g(x) + h(x)] = \frac{d}{dx} [f(x)]+\frac{d}{dx} [g(x)] +\frac{d}{dx} [h(x)]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29%2Bg%28x%29%20%2B%20h%28x%29%5D%20%3D%20%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bf%28x%29%5D%2B%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bg%28x%29%5D%20%2B%5Cfrac%7Bd%7D%7Bdx%7D%20%5Bh%28x%29%5D)
Now, each derivative is found by applying the derivative rules when appropriate:
Given
(Derivative of a arcsine function/Chain rule)
Given
(Derivative of a power function)
Given
(Derivative of a power function)
(Derivative for a sum of functions/Result)
<u>Given:</u>
A triangular piece is cut out of a rectangular piece of paper to make the class banner.
<u>To find:</u>
The area of the class banner.
<u>Solution:</u>
The rectangular piece of paper is 14 inches long and 
inches wide.
From the given diagram, the triangle has a base length of the same 8 inches and has a height of 
inches long.
To determine the area of the banner, we subtract the area of the triangle from the area of the rectangle.
The area of a triangle 
The area of the triangle 
square inches.
The area of a rectangle 
The area of the rectangle 
square inches.
The area of the class banner 
square inches.
So the banner has an area of 100 square inches which is the first option.
Answer:
(3, - 25 )
Step-by-step explanation:
Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
The the x- coordinate of the turning point is
x = - 
Given
y = (x + 2)(x - 8) ← expand factors using FOIL
= x² - 6x - 16 ← in standard form
with a = 1 and b = - 6, thus
x = - 
= 3
Substitute x = 3 into the equation for corresponding value of y
y = (3 + 2)(3 - 8) = 5(- 5) = - 25
turning point at (3, - 25 )
We basically have to cancel values on both sides until they are both on common ground.
7 + 3x = 5x + 13
-7 from both sides...
3x = 5x + 6
-5x from both sides...
-2x = 6
/-2 from both sides...
x = -3
Hope this helps!
