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ln(coth(x/2))
The derivative of the function/ ln(coth(x/2))

Derivative of ln(coth(x/2))

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   /    /x\\
log|coth|-||
   \    \2//
log⁡(coth⁡(x2))\log{\left(\coth{\left(\frac{x}{2} \right)} \right)} 
d /   /    /x\\\
--|log|coth|-|||
dx\   \    \2///
ddxlog⁡(coth⁡(x2))\frac{d}{d x} \log{\left(\coth{\left(\frac{x}{2} \right)} \right)}
Transform
The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       -1         
------------------
      /x\     2/x\
2*coth|-|*sinh |-|
      \2/      \2/
−12sinh⁡2(x2)coth⁡(x2)- \frac{1}{2 \sinh^{2}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}
Simplify
The second derivative [src] 
      /x\          1       
2*cosh|-| - ---------------
      \2/       /x\     /x\
            coth|-|*sinh|-|
                \2/     \2/
---------------------------
           /x\     3/x\    
     4*coth|-|*sinh |-|    
           \2/      \2/
2cosh⁡(x2)−1sinh⁡(x2)coth⁡(x2)4sinh⁡3(x2)coth⁡(x2)\frac{2 \cosh{\left(\frac{x}{2} \right)} - \frac{1}{\sinh{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}}{4 \sinh^{3}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}
Simplify
The third derivative [src] 
                              2/x\            /x\    
                        3*cosh |-|      3*cosh|-|    
            1                  \2/            \2/    
1 - ----------------- - ---------- + ----------------
        2/x\     4/x\        2/x\        /x\     3/x\
    coth |-|*sinh |-|    sinh |-|    coth|-|*sinh |-|
         \2/      \2/         \2/        \2/      \2/
-----------------------------------------------------
                        /x\     2/x\                 
                  4*coth|-|*sinh |-|                 
                        \2/      \2/
1−3cosh⁡2(x2)sinh⁡2(x2)+3cosh⁡(x2)sinh⁡3(x2)coth⁡(x2)−1sinh⁡4(x2)coth⁡2(x2)4sinh⁡2(x2)coth⁡(x2)\frac{1 - \frac{3 \cosh^{2}{\left(\frac{x}{2} \right)}}{\sinh^{2}{\left(\frac{x}{2} \right)}} + \frac{3 \cosh{\left(\frac{x}{2} \right)}}{\sinh^{3}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}} - \frac{1}{\sinh^{4}{\left(\frac{x}{2} \right)} \coth^{2}{\left(\frac{x}{2} \right)}}}{4 \sinh^{2}{\left(\frac{x}{2} \right)} \coth{\left(\frac{x}{2} \right)}}
Simplify
The graph
Derivative of ln(coth(x/2))
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