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)
Answer:

Step-by-step explanation:
<em>Let P(W) represents the probability that Paul wins</em>
<em>Let P(W') represents the probability that Paul does not win</em>
Given

Required

In probability, the sum of opposite probability equals 1;
This implies that

Substitute
in the above equation
becomes

Subtract
from both sides


Solve fraction (start by taking the LCM)



Hence, the probability that Paul doesn't win is 
Answer: x= 10
Step-by-step explanation:
Same side exterior angles sum to 180.
Using this axiom we can say that
142+ (3x+8) = 180
Add like terms on the left side
150+ 3x = 180
Subtract 150 from both sides
3x = 30
Divide both sides by 3
X= 10