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The derivative of the function/ log(log((x+1)/(x-1),5),2)

Derivative of log(log((x+1)/(x-1),5),2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   /   /x + 1   \   \
log|log|-----, 5|, 2|
   \   \x - 1   /   /
log⁡(log⁡(x+1x−1))\log{\left(\log{\left(\frac{x + 1}{x - 1} \right)} \right)} 
log(log((x + 1)/(x - 1), 5), 2)
The graph
02468-8-6-4-2-1010-1010
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
        /  1      x + 1  \
(x - 1)*|----- - --------|
        |x - 1          2|
        \        (x - 1) /
--------------------------
             /x + 1   \   
  (x + 1)*log|-----, 5|   
             \x - 1   /
(x−1)(1x−1−x+1(x−1)2)(x+1)log⁡(x+1x−1)\frac{\left(x - 1\right) \left(\frac{1}{x - 1} - \frac{x + 1}{\left(x - 1\right)^{2}}\right)}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}
Simplify
The second derivative [src] 
             /                   /    1 + x \       \       
             |                   |1 - ------|*log(5)|       
/    1 + x \ |    1       1      \    -1 + x/       |       
|1 - ------|*|- ----- - ------ - -------------------|*log(5)
\    -1 + x/ |  1 + x   -1 + x              /1 + x \|       
             |                   (1 + x)*log|------||       
             \                              \-1 + x//       
------------------------------------------------------------
                               /1 + x \                     
                    (1 + x)*log|------|                     
                               \-1 + x/
(1−x+1x−1)(−(1−x+1x−1)log⁡(5)(x+1)log⁡(x+1x−1)−1x+1−1x−1)log⁡(5)(x+1)log⁡(x+1x−1)\frac{\left(1 - \frac{x + 1}{x - 1}\right) \left(- \frac{\left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}} - \frac{1}{x + 1} - \frac{1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}
Simplify
The third derivative [src] 
             /                                                        2                                                               \       
             |                                            /    1 + x \     2        /    1 + x \               /    1 + x \           |       
             |                                          2*|1 - ------| *log (5)   3*|1 - ------|*log(5)      3*|1 - ------|*log(5)    |       
/    1 + x \ |   2           2              2             \    -1 + x/              \    -1 + x/               \    -1 + x/           |       
|1 - ------|*|-------- + --------- + ---------------- + ----------------------- + --------------------- + ----------------------------|*log(5)
\    -1 + x/ |       2           2   (1 + x)*(-1 + x)           2    2/1 + x \            2    /1 + x \                       /1 + x \|       
             |(1 + x)    (-1 + x)                        (1 + x) *log |------|     (1 + x) *log|------|   (1 + x)*(-1 + x)*log|------||       
             \                                                        \-1 + x/                 \-1 + x/                       \-1 + x//       
----------------------------------------------------------------------------------------------------------------------------------------------
                                                                        /1 + x \                                                              
                                                             (1 + x)*log|------|                                                              
                                                                        \-1 + x/
(1−x+1x−1)(2(1−x+1x−1)2log⁡(5)2(x+1)2log⁡(x+1x−1)2+3(1−x+1x−1)log⁡(5)(x+1)2log⁡(x+1x−1)+3(1−x+1x−1)log⁡(5)(x−1)(x+1)log⁡(x+1x−1)+2(x+1)2+2(x−1)(x+1)+2(x−1)2)log⁡(5)(x+1)log⁡(x+1x−1)\frac{\left(1 - \frac{x + 1}{x - 1}\right) \left(\frac{2 \left(1 - \frac{x + 1}{x - 1}\right)^{2} \log{\left(5 \right)}^{2}}{\left(x + 1\right)^{2} \log{\left(\frac{x + 1}{x - 1} \right)}^{2}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x + 1\right)^{2} \log{\left(\frac{x + 1}{x - 1} \right)}} + \frac{3 \left(1 - \frac{x + 1}{x - 1}\right) \log{\left(5 \right)}}{\left(x - 1\right) \left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}} + \frac{2}{\left(x + 1\right)^{2}} + \frac{2}{\left(x - 1\right) \left(x + 1\right)} + \frac{2}{\left(x - 1\right)^{2}}\right) \log{\left(5 \right)}}{\left(x + 1\right) \log{\left(\frac{x + 1}{x - 1} \right)}}
Simplify
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