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The derivative of the function/ 6arctg((lnx)/2)

Derivative of 6arctg((lnx)/2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
      /log(x)\
6*atan|------|
      \  2   /
$$6 \operatorname{atan}{\left(\frac{\log{\left(x \right)}}{2} \right)}$$ 
6*atan(log(x)/2)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       3       
---------------
  /       2   \
  |    log (x)|
x*|1 + -------|
  \       4   /
$$\frac{3}{x \left(\frac{\log{\left(x \right)}^{2}}{4} + 1\right)}$$
Simplify
The second derivative [src] 
    /      2*log(x) \
-12*|1 + -----------|
    |           2   |
    \    4 + log (x)/
---------------------
    2 /       2   \  
   x *\4 + log (x)/
$$- \frac{12 \left(1 + \frac{2 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 4}\right)}{x^{2} \left(\log{\left(x \right)}^{2} + 4\right)}$$
Simplify
The third derivative [src] 
   /                                       2      \
   |         1          3*log(x)      4*log (x)   |
24*|1 - ----------- + ----------- + --------------|
   |           2             2                   2|
   |    4 + log (x)   4 + log (x)   /       2   \ |
   \                                \4 + log (x)/ /
---------------------------------------------------
                   3 /       2   \                 
                  x *\4 + log (x)/
$$\frac{24 \left(1 + \frac{3 \log{\left(x \right)}}{\log{\left(x \right)}^{2} + 4} - \frac{1}{\log{\left(x \right)}^{2} + 4} + \frac{4 \log{\left(x \right)}^{2}}{\left(\log{\left(x \right)}^{2} + 4\right)^{2}}\right)}{x^{3} \left(\log{\left(x \right)}^{2} + 4\right)}$$
Simplify
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