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 \frac{(-1)\cdot (1+x)-(1)\cdot (1-x)}{(1+x)^{2}}](https://tex.z-dn.net/?f=y%27%20%3D%20%5Cfrac%7B1%7D%7B2%5Ccdot%20%5Csqrt%7B%5Cfrac%7B1-x%7D%7B1%2Bx%7D%20%7D%7D%5Ccdot%20%5Cfrac%7B%28-1%29%5Ccdot%20%281%2Bx%29-%281%29%5Ccdot%20%281-x%29%7D%7B%281%2Bx%29%5E%7B2%7D%7D)
![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)
![y' = -\frac{1}{(1-x)\cdot (1+x)^{3/2}}](https://tex.z-dn.net/?f=y%27%20%3D%20-%5Cfrac%7B1%7D%7B%281-x%29%5Ccdot%20%281%2Bx%29%5E%7B3%2F2%7D%7D)
The first derivative of
is
.
D. -4(x+9)
For this you distribute the number outside the parentheses to both numbers inside.
A. 4(x-9)=
4x-36
B. 2(2x-18)=
4x-36
C. -2(2x-18)=
-4x+36
D. -4(x+9)=
-4x-36
Therefore, D is the answer
Answer:
they are congruent because SAS
Step-by-step explanation:
Answer: 2
Step-by-step explanation:
3/5 of 30 = 18(AL)
2/6 of 30 = 10 (ML)
18+10 = 28 (AL+ ML)
the remainder
30-28 = 2 (CL)