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Derivative of sqrt(log((x^-1),2))

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
    ___________
   /    /1   \ 
  /  log|-, 2| 
\/      \x   / 
$$\sqrt{\log{\left(\frac{1}{x} \right)}}$$
sqrt(log(1/x, 2))
The graph
The first derivative [src]
        -1         
-------------------
        ___________
       /    /1   \ 
2*x*  /  log|-, 2| 
    \/      \x   / 
$$- \frac{1}{2 x \sqrt{\log{\left(\frac{1}{x} \right)}}}$$
The second derivative [src]
           1        
   2 - ---------    
          /1   \    
       log|-, 2|    
          \x   /    
--------------------
         ___________
   2    /    /1   \ 
4*x *  /  log|-, 2| 
     \/      \x   / 
$$\frac{2 - \frac{1}{\log{\left(\frac{1}{x} \right)}}}{4 x^{2} \sqrt{\log{\left(\frac{1}{x} \right)}}}$$
The third derivative [src]
          3              3     
-1 - ------------ + -----------
          2/1   \        /1   \
     8*log |-, 2|   4*log|-, 2|
           \x   /        \x   /
-------------------------------
              ___________      
        3    /    /1   \       
       x *  /  log|-, 2|       
          \/      \x   /       
$$\frac{-1 + \frac{3}{4 \log{\left(\frac{1}{x} \right)}} - \frac{3}{8 \log{\left(\frac{1}{x} \right)}^{2}}}{x^{3} \sqrt{\log{\left(\frac{1}{x} \right)}}}$$