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atan(log(1/x))

Derivada de atan(log(1/x))

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
    /   /1\\
atan|log|-||
    \   \x//
$$\operatorname{atan}{\left(\log{\left(\frac{1}{x} \right)} \right)}$$
atan(log(1/x))
Gráfica
Primera derivada [src]
      -1       
---------------
  /       2/1\\
x*|1 + log |-||
  \        \x//
$$- \frac{1}{x \left(\log{\left(\frac{1}{x} \right)}^{2} + 1\right)}$$
Segunda derivada [src]
           /1\  
      2*log|-|  
           \x/  
1 - ----------- 
           2/1\ 
    1 + log |-| 
            \x/ 
----------------
 2 /       2/1\\
x *|1 + log |-||
   \        \x//
$$\frac{1 - \frac{2 \log{\left(\frac{1}{x} \right)}}{\log{\left(\frac{1}{x} \right)}^{2} + 1}}{x^{2} \left(\log{\left(\frac{1}{x} \right)}^{2} + 1\right)}$$
Tercera derivada [src]
  /                          2/1\             /1\ \
  |                     4*log |-|        3*log|-| |
  |          1                \x/             \x/ |
2*|-1 + ----------- - -------------- + -----------|
  |            2/1\                2          2/1\|
  |     1 + log |-|   /       2/1\\    1 + log |-||
  |             \x/   |1 + log |-||            \x/|
  \                   \        \x//               /
---------------------------------------------------
                   3 /       2/1\\                 
                  x *|1 + log |-||                 
                     \        \x//                 
$$\frac{2 \left(-1 + \frac{3 \log{\left(\frac{1}{x} \right)}}{\log{\left(\frac{1}{x} \right)}^{2} + 1} + \frac{1}{\log{\left(\frac{1}{x} \right)}^{2} + 1} - \frac{4 \log{\left(\frac{1}{x} \right)}^{2}}{\left(\log{\left(\frac{1}{x} \right)}^{2} + 1\right)^{2}}\right)}{x^{3} \left(\log{\left(\frac{1}{x} \right)}^{2} + 1\right)}$$
Gráfico
Derivada de atan(log(1/x))