Answer:
The first derivative of
is
.
Step-by-step explanation:
Let
. we can determine its first derivative by Rule for the Square Root Function, Rule for Power Function, Rule of Chain and Rule for the Addition of Functions, Rule for the Subtraction of Functions, Rule for the Division of Functions:

![y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} }\cdot \left[\frac{-1-x-1+x}{(1+x)^{2}} \right]](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1%2Bx%7D%7B1-x%7D%20%7D%5Ccdot%20%5Cleft%5B%5Cfrac%7B-1-x-1%2Bx%7D%7B%281%2Bx%29%5E%7B2%7D%7D%20%5Cright%5D)
![y' = \frac{1}{2}\cdot \sqrt{\frac{1+x}{1-x} } \cdot \left[-\frac{2}{(1+x)^{2}} \right]](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1%2Bx%7D%7B1-x%7D%20%7D%20%5Ccdot%20%5Cleft%5B-%5Cfrac%7B2%7D%7B%281%2Bx%29%5E%7B2%7D%7D%20%5Cright%5D)

The first derivative of
is
.
Answer: 2 + 2 = 4
Step-by-step explanation: Let's say you have 2 cars, and you friend has 2 cars, for your birthday, your friend gives you his 2 cars, so now in total you have 4 cars, hope this helped! -Mason
Answer:
See below
Step-by-step explanation:
<u><em>Proof:</em></u>
<u><em>Statements </em></u> | <u><em>Reasons</em></u>
AD ≅ BC | Given
AD ║ BC | Given
AC ≅ AC | Reflexive Property
∠DAC ≅ ∠ACB | If 2 || lines are cut by a trans., the | alternate interior ∠s are congruent.
ΔADC ≅ ΔBCA | S.A.S Postulate
BA ≅ DC | Corresponding sides of congruent Δs
So, quad. ABCD is a ║gm | If a quad. has its opposite sides
| congruent, the quad. is a parallelogram.
Answer:
36/40, 47/101, 192
Step-by-step explanation:
(a)The numerator (top number of the fraction) is adding up by odd numbers in order.
From 1/40 to 4/40 you add 3, from 4/40 to 9/40 you add 5, from 9/40 to 16/40 you add 7, and from 16/40 to 25/40 you add 9.
The next number to add would logically be 11. So from 25/40 you would go to 36/40.
36/40 is your next fraction.
(b)
3+4=7,4+7=11,7+11=18,11+18=29,18+29=47
(c) 1*2=2,2*2=4,2*4=8,4*8=32,8*32=256,32*256=8,192