second derivation of x+1\x-1

Question

second derivation of x+1\x-1

Answer 1

 

First derivative.... need the quotient rule:

(x-1)(1) - (x+1)(1)               x - 1 - x - 1                   -2

------------------------ =     --------------------- =  ------------- 

         (x-1)^2                        (x-1)^2                     (x-1)^2

 

The second derivative... again by quotient rule:

 

(x-1)^2 * 0 - (-2)*2(x-1)*(1)             4(x-1)                               4

---------------------------------- = ---------------------- = ---------------------

     (x-1)^4                                      (x-1)^4                          (x-1)^3

 

 

Answer 2

I assume you really meant

 

f(x) = (x + 1) / (x - 1),

 

which is not the same as 

 

x + 1/x - 1.

 

Please use parentheses.

 

f'(x) = [1(x - 1) - (x + 1)(1)] / (x - 1)² = -2 / (x - 1)²

 

f''(x) = -2(-2) / (x - 1)³ = 4 / (x - 1)³