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Derivada de:
Derivada de 1/(x+3)
Derivada de x/a
Derivada de 1/x^(1/2)
Derivada de x^-(4/5)
Expresiones idénticas
(x/(ln(uno +x^ dos)/(uno +x^ dos)))*arсctg(x/(ln(uno +x^ dos)/(uno +x^ dos)))
(x dividir por (ln(1 más x al cuadrado ) dividir por (1 más x al cuadrado ))) multiplicar por arсctg(x dividir por (ln(1 más x al cuadrado ) dividir por (1 más x al cuadrado )))
(x dividir por (ln(uno más x en el grado dos) dividir por (uno más x en el grado dos))) multiplicar por arсctg(x dividir por (ln(uno más x en el grado dos) dividir por (uno más x en el grado dos)))
(x/(ln(1+x2)/(1+x2)))*arсctg(x/(ln(1+x2)/(1+x2)))
x/ln1+x2/1+x2*arсctgx/ln1+x2/1+x2
(x/(ln(1+x²)/(1+x²)))*arсctg(x/(ln(1+x²)/(1+x²)))
(x/(ln(1+x en el grado 2)/(1+x en el grado 2)))*arсctg(x/(ln(1+x en el grado 2)/(1+x en el grado 2)))
(x/(ln(1+x^2)/(1+x^2)))arсctg(x/(ln(1+x^2)/(1+x^2)))
(x/(ln(1+x2)/(1+x2)))arсctg(x/(ln(1+x2)/(1+x2)))
x/ln1+x2/1+x2arсctgx/ln1+x2/1+x2
x/ln1+x^2/1+x^2arсctgx/ln1+x^2/1+x^2
(x dividir por (ln(1+x^2) dividir por (1+x^2)))*arсctg(x dividir por (ln(1+x^2) dividir por (1+x^2)))
Expresiones semejantes
(x/(ln(1-x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))
(x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1-x^2)/(1+x^2)))
(x/(ln(1+x^2)/(1-x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))
(x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1-x^2)))
Expresiones con funciones
ln
ln(x/5)
ln(×)
ln(x+10)^10
ln(arcsinx)
ln2u
ln
ln(x/5)
ln(×)
ln(x+10)^10
ln(arcsinx)
ln2u

Derivada de la función/ (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))

Derivada de (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))

Solución

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

                                                                                                  /                          2 /                     /     2\\\
                                                                                                  |                  /     2\  |     2*x      2*x*log\1 + x /||
                                                                                                  |                x*\1 + x / *|- --------- + ---------------||
                                                                                                  |                            |          2              2   ||
                                                                                              2   |                            |  /     2\       /     2\    ||
                                                                                         1 + x    |      1                     \  \1 + x /       \1 + x /    /|
/                          2 /                     /     2\\\                       x*-----------*|------------- + -------------------------------------------|
|                  /     2\  |     2*x      2*x*log\1 + x /||                            /     2\ |/   /     2\\                      2/     2\               |
|                x*\1 + x / *|- --------- + ---------------||                         log\1 + x / ||log\1 + x /|                   log \1 + x /               |
|                            |          2              2   ||                                     ||-----------|                                              |
|                            |  /     2\       /     2\    ||                                     ||        2  |                                              |
|      1                     \  \1 + x /       \1 + x /    /|     /      x      \                 \\   1 + x   /                                              /
|------------- + -------------------------------------------|*acot|-------------| - ---------------------------------------------------------------------------
|/   /     2\\                      2/     2\               |     |/   /     2\\|                                                2                             
||log\1 + x /|                   log \1 + x /               |     ||log\1 + x /||                                      2 /     2\                              
||-----------|                                              |     ||-----------||                                     x *\1 + x /                              
||        2  |                                              |     ||        2  ||                                 1 + ------------                             
\\   1 + x   /                                              /     \\   1 + x   //                                        2/     2\                             
                                                                                                                      log \1 + x /

- \frac{x \frac{x^{2} + 1}{\log{\left(x^{2} + 1 \right)}} \left(\frac{x \left(x^{2} + 1\right)^{2} \left(\frac{2 x \log{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 x}{\left(x^{2} + 1\right)^{2}}\right)}{\log{\left(x^{2} + 1 \right)}^{2}} + \frac{1}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}}\right)}{\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1} + \left(\frac{x \left(x^{2} + 1\right)^{2} \left(\frac{2 x \log{\left(x^{2} + 1 \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{2 x}{\left(x^{2} + 1\right)^{2}}\right)}{\log{\left(x^{2} + 1 \right)}^{2}} + \frac{1}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}}\right) \operatorname{acot}{\left(\frac{x}{\frac{1}{x^{2} + 1} \log{\left(x^{2} + 1 \right)}} \right)}

Simplificar

Segunda derivada [src]

  /                                                                                                                                                                                                                           /                                                                                                             /            2 /        /     2\\\ /                  2   \\\
  |                                                                                                                                                                                                                           |                                                                                                    /     2\ |     2   2*x *\-1 + log\1 + x //| |       2       2*x    |||
  |                                                                                                                                                                                                                           |                                                                                                    \1 + x /*|1 + x  + -----------------------|*|1 + 3*x  - -----------|||
  |                                                                                                                                                                                                                           |                        2       2 /        /     2\\      2    /     2\      2 /        /     2\\            |                  /     2\      | |              /     2\|||
  |                                                                                                                                                                                                                2 /     2\ |         /     2\    6*x     4*x *\-1 + log\1 + x //   4*x *log\1 + x /   4*x *\-1 + log\1 + x //            \               log\1 + x /      / \           log\1 + x //||
  |                                                                                                                                                                                                               x *\1 + x /*|3 - 3*log\1 + x / - ------ - ----------------------- + ---------------- + ----------------------- + --------------------------------------------------------------------||
  |                                    2                                                                                                                                                                                      |                         2                 2                     2          /     2\    /     2\                       /               2\                               ||
  |  /            2 /        /     2\\\                                                                                                                                                                                       |                    1 + x             1 + x                 1 + x           \1 + x /*log\1 + x /                       |     2 /     2\ |                               ||
  |  |     2   2*x *\-1 + log\1 + x //|      /                                                                                                        2 /         1     \ /        /     2\\\                                 |                                                                                                                       |    x *\1 + x / |    /     2\                   ||
  |  |1 + x  + -----------------------|      |                                                                                                     2*x *|1 - -----------|*\-1 + log\1 + x //|                                 |                                                                                                                       |1 + ------------|*log\1 + x /                   ||
  |  |                  /     2\      |      |                         2       2    /     2\      2 /        /     2\\      2 /        /     2\\        |       /     2\|                   |     /   /     2\\               |                                                                                                                       |       2/     2\|                               ||
  |  \               log\1 + x /      /      |          /     2\    6*x     4*x *log\1 + x /   2*x *\-1 + log\1 + x //   2*x *\-1 + log\1 + x //        \    log\1 + x //                   |     | x*\1 + x /|               \                                                                                                                       \    log \1 + x //                               /|
2*|- ----------------------------------- + x*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - ----------------------- + -----------------------------------------|*acot|-----------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |                           2              |                          2             2                      2             /     2\    /     2\                           2                 |     |   /     2\|                                                                               /               2\                                                                                        |
  |                 2 /     2\               \                     1 + x         1 + x                  1 + x              \1 + x /*log\1 + x /                      1 + x                  /     \log\1 + x //                                                                               |     2 /     2\ |                                                                                        |
  |                x *\1 + x /                                                                                                                                                                                                                                                                |    x *\1 + x / |    /     2\                                                                            |
  |            1 + ------------                                                                                                                                                                                                                                                               |1 + ------------|*log\1 + x /                                                                            |
  |                   2/     2\                                                                                                                                                                                                                                                               |       2/     2\|                                                                                        |
  \                log \1 + x /                                                                                                                                                                                                                                                               \    log \1 + x //                                                                                        /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                  2/     2\                                                                                                                                                                                              
                                                                                                                                                                                               log \1 + x /

\frac{2 \left(\frac{x^{2} \left(x^{2} + 1\right) \left(- \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} + \frac{\left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - 3 \log{\left(x^{2} + 1 \right)} + 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + x \left(\frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right) \operatorname{acot}{\left(\frac{x \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} \right)} - \frac{\left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)^{2}}{\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1}\right)}{\log{\left(x^{2} + 1 \right)}^{2}}

Simplificar

Tercera derivada [src]

  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  2                                   \                                                                                                                                                                                                                                                                                                                                                                                                              \
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                                                       /                      2       2    /     2\\        /                        2        2    /     2\\                                                        /            2 /        /     2\\\ /        2                 4                              4           2 /     2\\                                                                                                          /                      2       2    /     2\\                                            /                  2   \ /                         2       2    /     2\      2 /        /     2\\      2 /        /     2\\\                2 /                  2   \  /            2 /        /     2\\\|                                                                                                                                                                                                                                                                                                                                                                                                              |
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                                                     2 |       /     2\    6*x     4*x *log\1 + x /|      2 |         /     2\   22*x     12*x *log\1 + x /|                                                        |     2   2*x *\-1 + log\1 + x //| |/     2\       4      12*x           2 /     2\      12*x        10*x *\1 + x /|                                                            2 /         1     \ /        /     2\\      2 |       /     2\    6*x     4*x *log\1 + x /|                                 2 /     2\ |       2       2*x    | |          /     2\    6*x     4*x *log\1 + x /   4*x *\-1 + log\1 + x //   4*x *\-1 + log\1 + x //|      2 /     2\  |       2       2*x    |  |     2   2*x *\-1 + log\1 + x //||                                                                                                                                                                                                                                    /                                                                                                             /            2 /        /     2\\\ /                  2   \\|
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                                                  8*x *|1 - log\1 + x / - ------ + ----------------|   2*x *|9 - 6*log\1 + x / - ------ + -----------------|                                                        |1 + x  + -----------------------|*|\1 + x /  + 4*x  - ----------- + 10*x *\1 + x / + ------------ - --------------|                                                         2*x *|1 - -----------|*\-1 + log\1 + x //   8*x *|1 - log\1 + x / - ------ + ----------------|                              4*x *\1 + x /*|1 + 3*x  - -----------|*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - -----------------------|   4*x *\1 + x / *|1 + 3*x  - -----------| *|1 + x  + -----------------------||                                                                                                                                                                                                                                    |                                                                                                    /     2\ |     2   2*x *\-1 + log\1 + x //| |       2       2*x    |||
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          |                         2        2    /     2\        |                       2             2     |        |                         2              2     |      4 /        /     2\\       2 /        /     2\\   |                  /     2\      | |                      /     2\                       2/     2\       /     2\  |       4 /        /     2\\       2 /        /     2\\        |       /     2\|                           |                       2             2     |       4 /        /     2\\                 |              /     2\| |                          2             2                      2             /     2\    /     2\ |                  |              /     2\|  |                  /     2\      ||                                                                                                                                                                                                                                    |                                                                                                    \1 + x /*|1 + x  + -----------------------|*|1 + 3*x  - -----------|||
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /     2\ |          /     2\   18*x     12*x *log\1 + x /        \                  1 + x         1 + x      /        \                    1 + x          1 + x      /   8*x *\-1 + log\1 + x //   14*x *\-1 + log\1 + x //   \               log\1 + x /      / \                   log\1 + x /                    log \1 + x /    log\1 + x /  /   24*x *\-1 + log\1 + x //   14*x *\-1 + log\1 + x //        \    log\1 + x //                           \                  1 + x         1 + x      /   24*x *\-1 + log\1 + x //                 \           log\1 + x // \                     1 + x         1 + x                  1 + x              \1 + x /*log\1 + x / /                  \           log\1 + x //  \               log\1 + x /      /|                                                                                                                                                                                                 /            2 /        /     2\\\ |                        2       2 /        /     2\\      2    /     2\      2 /        /     2\\            |                  /     2\      | |              /     2\|||
  |/                                                       /                                                                                                                                                                                                   /                      2       2    /     2\\                                                                                                                                                                               \                                                                                                \                     x*\1 + x /*|-3 + 3*log\1 + x / + ------ - ----------------- - -------------------------------------------------- + ----------------------------------------------------- + ----------------------- + ------------------------ - -------------------------------------------------------------------------------------------------------------------- - ------------------------ - ------------------------ + ----------------------------------------- + -------------------------------------------------- + ------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------|                                                                                                                                                                                                 |     2   2*x *\-1 + log\1 + x //| |         /     2\    6*x     4*x *\-1 + log\1 + x //   4*x *log\1 + x /   4*x *\-1 + log\1 + x //            \               log\1 + x /      / \           log\1 + x //||
  ||                                                       |                                                                                                                                                                                                   |       /     2\    6*x     4*x *log\1 + x /|                                                                   2 /         1     \ /        /     2\\                                2 /         1     \ /        /     2\\|                                                                                                |                                |                          2              2                                   2                                                      2                                         2                        2                                                       /               2\                                                                   2                   /     2\    /     2\                            2                                   /     2\    /     2\                           2                                                                       /               2\                                                                                                              2                                  |                                          /                                                                                                        2 /         1     \ /        /     2\\\   3*x*|1 + x  + -----------------------|*|3 - 3*log\1 + x / - ------ - ----------------------- + ---------------- + ----------------------- + --------------------------------------------------------------------||
  ||                                                       |                                                                                                                                                                                                 3*|1 - log\1 + x / - ------ + ----------------|                                                                2*x *|1 - -----------|*\-1 + log\1 + x //                             2*x *|1 - -----------|*\-1 + log\1 + x //|                                                                                                |                                |                     1 + x          1 + x                               1 + x                                                  1 + x                                  /     2\                    1 + x                                                        |     2 /     2\ |                                                           /     2\     /     2\       \1 + x /*log\1 + x /                       1 + x                                    \1 + x /*log\1 + x /                   /     2\     2/     2\                                                          |     2 /     2\ |                                                                                            /               2\                                   |                                          |                                                                                                     2*x *|1 - -----------|*\-1 + log\1 + x //|       |                  /     2\      | |                         2                 2                     2          /     2\    /     2\                       /               2\                               ||
  ||                                                       |                             /     2\                     /                      2       2    /     2\\                      /                               2                      2        \     |                       2             2     |       2       2 /        /     2\\      2 /        /     2\\        |       /     2\|                         2 /        /     2\\        |       /     2\|                   |                                                                                                |                                |                                                                                                                                                                      \1 + x /                                                                                 |    x *\1 + x / |    /     2\                                               \1 + x / *log\1 + x /                                                                                                                                  \1 + x / *log \1 + x /                                                          |    x *\1 + x / |    2/     2\                                                                               |     2 /     2\ |                                   |       /            2 /        /     2\\\ |                         2       2    /     2\      2 /        /     2\\      2 /        /     2\\        |       /     2\|                   |       \               log\1 + x /      / |                    1 + x             1 + x                 1 + x           \1 + x /*log\1 + x /                       |     2 /     2\ |                               ||
  ||                                                     2 |          /     2\   -1 + log\1 + x /   /         1     \ |       /     2\    6*x     4*x *log\1 + x /|   /        /     2\\ |          1                 4*x                    2*x         |     \                  1 + x         1 + x      /    4*x     2*x *\-1 + log\1 + x //   6*x *\-1 + log\1 + x //        \    log\1 + x //                      6*x *\-1 + log\1 + x //        \    log\1 + x //                   |                                                          2 /         1     \ /        /     2\\|                                |                                                                                                                                                                                                                                                               |1 + ------------|*log\1 + x /                                                                                                                                                                                                                                                                                      |1 + ------------|*log \1 + x /                                                                               |    x *\1 + x / |     3/     2\                     |       |     2   2*x *\-1 + log\1 + x //| |          /     2\    6*x     4*x *log\1 + x /   2*x *\-1 + log\1 + x //   2*x *\-1 + log\1 + x //        \    log\1 + x //                   |                                          |                                                                                                                       |    x *\1 + x / |    /     2\                   ||
  ||                                                  2*x *|-5 + 2*log\1 + x / + ---------------- + |1 - -----------|*|1 - log\1 + x / - ------ + ----------------| + \-1 + log\1 + x //*|-1 + ----------- - --------------------- + --------------------| - ----------------------------------------------- + ------ - ----------------------- - ----------------------- - ----------------------------------------- + ----------------------- + -----------------------------------------|                                                       6*x *|1 - -----------|*\-1 + log\1 + x //|                                |                                                                                                                                                                                                                                                               |       2/     2\|                                                                                                                                                                                                                                                                                                  |       2/     2\|                                                                                            |1 + ------------| *log \1 + x /                     |   3*x*|1 + x  + -----------------------|*|-3 + 3*log\1 + x / + ------ - ---------------- + ----------------------- - ----------------------- + -----------------------------------------|                                          |                                                                                                                       |1 + ------------|*log\1 + x /                   ||
  ||                         2        2    /     2\        |                          /     2\      |       /     2\| |                       2             2     |                      |        /     2\   /     2\    2/     2\   /     2\    /     2\|                        /     2\                          2                 2            /     2\    2/     2\                           2                      /     2\    /     2\               /     2\    /     2\          |      2 /        /     2\\      2 /        /     2\\        |       /     2\|                   |     /   /     2\\              |                                                                                                                                                                                                                                                               \    log \1 + x //                                                                                                                                                                                                                                                                                                  \    log \1 + x //                                                                                            |       2/     2\|                                   |       |                  /     2\      | |                          2             2                      2             /     2\    /     2\                           2                 |                                          |                                                                                                                       |       2/     2\|                               ||
  ||          /     2\   18*x     12*x *log\1 + x /        \                       log\1 + x /      \    log\1 + x // \                  1 + x         1 + x      /                      \     log\1 + x /   \1 + x /*log \1 + x /   \1 + x /*log\1 + x //                     log\1 + x /                     1 + x             1 + x             \1 + x /*log \1 + x /                      1 + x                       \1 + x /*log\1 + x /               \1 + x /*log\1 + x /          /   6*x *\-1 + log\1 + x //   6*x *\-1 + log\1 + x //        \    log\1 + x //                   |     | x*\1 + x /|              \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \    log \1 + x //                                   /       \               log\1 + x /      / \                     1 + x         1 + x                  1 + x              \1 + x /*log\1 + x /                      1 + x                  /                                          \                                                                                                                       \    log \1 + x //                               /|
2*||-3 + 3*log\1 + x / + ------ - ----------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------- - ----------------------- + -----------------------------------------|*acot|-----------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  ||                          2              2                                                                                                                                                                                                                             2                                                                                                                                                                                                                                 2             /     2\    /     2\                           2                 |     |   /     2\|                                                                                                                                                                                                                                                                                                                                                                      /               2\                                                                                                                                                                                                                                                                                                                                                                                                                                                              /               2\                                                                                                                                                                                     /               2\                                                                                                     |
  |\                     1 + x          1 + x                                                                                                                                                                                                                         1 + x                                                                                                                                                                                                                             1 + x              \1 + x /*log\1 + x /                      1 + x                  /     \log\1 + x //                                                                                                                                                                                                                                                                                                                                                                      |     2 /     2\ |                                                                                                                                                                                                                                                                                                                                                                                                                                                              |     2 /     2\ |                                                                                                                                                                                     |     2 /     2\ |                                                                                                     |
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |    x *\1 + x / |    /     2\                                                                                                                                                                                                                                                                                                                                                                                                                                                  |    x *\1 + x / |    /     2\                                                                                                                                                                         |    x *\1 + x / |    /     2\                                                                                         |
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |1 + ------------|*log\1 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                  |1 + ------------|*log\1 + x /                                                                                                                                                                         |1 + ------------|*log\1 + x /                                                                                         |
  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |       2/     2\|                                                                                                                                                                                                                                                                                                                                                                                                                                                              |       2/     2\|                                                                                                                                                                                     |       2/     2\|                                                                                                     |
  \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  \    log \1 + x //                                                                                                                                                                                                                                                                                                                                                                                                                                                              \    log \1 + x //                                                                                                                                                                                     \    log \1 + x //                                                                                                     /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            log \1 + x /

\frac{2 \left(- \frac{x \left(x^{2} + 1\right) \left(\frac{8 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{24 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}} + \frac{24 x^{4} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}^{2}} + \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(x^{2} + 1\right)^{2} \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right)^{2} \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right)^{2} \log{\left(x^{2} + 1 \right)}^{3}} - \frac{4 x^{2} \left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} + \frac{14 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{14 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{8 x^{2} \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{x^{2} + 1} + \frac{8 x^{2} \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{2 x^{2} \left(\frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{22 x^{2}}{x^{2} + 1} - 6 \log{\left(x^{2} + 1 \right)} + 9\right)}{x^{2} + 1} - \frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{18 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3 - \frac{\left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(4 x^{4} - \frac{12 x^{4}}{\log{\left(x^{2} + 1 \right)}} + \frac{12 x^{4}}{\log{\left(x^{2} + 1 \right)}^{2}} + 10 x^{2} \left(x^{2} + 1\right) - \frac{10 x^{2} \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} + \left(x^{2} + 1\right)^{2}\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}}\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{3 x \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(- \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{4 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} + \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} + \frac{\left(x^{2} + 1\right) \left(3 x^{2} - \frac{2 x^{2}}{\log{\left(x^{2} + 1 \right)}} + 1\right) \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - 3 \log{\left(x^{2} + 1 \right)} + 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{3 x \left(\frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\log{\left(x^{2} + 1 \right)}} + x^{2} + 1\right) \left(\frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{6 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right)}{\left(\frac{x^{2} \left(x^{2} + 1\right)^{2}}{\log{\left(x^{2} + 1 \right)}^{2}} + 1\right) \log{\left(x^{2} + 1 \right)}} + \left(\frac{6 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} - \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{2 x^{2} \left(- \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{2 x^{2} \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{2 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{x^{2} + 1} + \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{6 x^{2} \left(\log{\left(x^{2} + 1 \right)} - 1\right)}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} + \frac{4 x^{2}}{x^{2} + 1} + \left(1 - \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right) + \left(\log{\left(x^{2} + 1 \right)} - 1\right) \left(\frac{2 x^{2}}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}} - \frac{4 x^{2}}{\left(x^{2} + 1\right) \log{\left(x^{2} + 1 \right)}^{2}} - 1 + \frac{1}{\log{\left(x^{2} + 1 \right)}}\right) + \frac{\log{\left(x^{2} + 1 \right)} - 1}{\log{\left(x^{2} + 1 \right)}} - \frac{3 \left(\frac{4 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} - \frac{6 x^{2}}{x^{2} + 1} - \log{\left(x^{2} + 1 \right)} + 1\right)}{\log{\left(x^{2} + 1 \right)}} + 2 \log{\left(x^{2} + 1 \right)} - 5\right)}{x^{2} + 1} - \frac{12 x^{2} \log{\left(x^{2} + 1 \right)}}{x^{2} + 1} + \frac{18 x^{2}}{x^{2} + 1} + 3 \log{\left(x^{2} + 1 \right)} - 3\right) \operatorname{acot}{\left(\frac{x \left(x^{2} + 1\right)}{\log{\left(x^{2} + 1 \right)}} \right)}\right)}{\log{\left(x^{2} + 1 \right)}^{2}}

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Derivada de (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))

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Derivada de (x/(ln(1+x^2)/(1+x^2)))*arсctg(x/(ln(1+x^2)/(1+x^2)))

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