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(ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(-2)
Derivada de la función/ (ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(-2)

Derivada de (ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(-2)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
           1            
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    /        /  2     \\
   2| 3      | x  + 1 ||
cot |x  + log|--------||
    |        |       2||
    \        \1 - 2*x //
1cot⁡2(x3+log⁡(x2+11−2x2))\frac{1}{\cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)}} 
cot(x^3 + log((x^2 + 1)/(1 - 2*x^2)))^(-2)
Gráfica
02468-8-6-4-2-1010-5000050000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                   /                  /               / 2    \\\
                                   |       /       2\ |  2*x      4*x*\x  + 1/||
                                   |       \1 - 2*x /*|-------- + ------------||
                                   |                  |       2             2 ||
   /         /        /  2     \\\ |                  |1 - 2*x    /       2\  ||
   |        2| 3      | x  + 1 ||| |   2              \           \1 - 2*x /  /|
-2*|-1 - cot |x  + log|--------|||*|3*x  + ------------------------------------|
   |         |        |       2||| |                       2                   |
   \         \        \1 - 2*x /// \                      x  + 1               /
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                                /        /  2     \\                            
                               3| 3      | x  + 1 ||                            
                            cot |x  + log|--------||                            
                                |        |       2||                            
                                \        \1 - 2*x //
−2(3x2+(1−2x2)(2x1−2x2+4x(x2+1)(1−2x2)2)x2+1)(−cot⁡2(x3+log⁡(x2+11−2x2))−1)cot⁡3(x3+log⁡(x2+11−2x2))- \frac{2 \left(3 x^{2} + \frac{\left(1 - 2 x^{2}\right) \left(\frac{2 x}{1 - 2 x^{2}} + \frac{4 x \left(x^{2} + 1\right)}{\left(1 - 2 x^{2}\right)^{2}}\right)}{x^{2} + 1}\right) \left(- \cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)} - 1\right)}{\cot^{3}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - 2 x^{2}} \right)} \right)}}
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Segunda derivada [src] 
                                   /                                        /             /     2\         2         2 /     2\                                                  \                                                                     \
                                   |                                        |           2*\1 + x /      8*x      16*x *\1 + x /        /       /     2\\        /       /     2\\|                                   2                                 |
                                   |                                        |      -1 + ---------- + --------- - --------------      2 |     2*\1 + x /|      2 |     2*\1 + x /||        /        /       /     2\\\                                  |
                                   |                                        |                   2            2               2    2*x *|-1 + ----------|   4*x *|-1 + ----------||        |        |     2*\1 + x /||                                  |
                                   |                                  2     |           -1 + 2*x     -1 + 2*x     /        2\          |             2 |        |             2 ||        |      2*|-1 + ----------||                                  |
                                   |       /        /       /     2\\\      |                                     \-1 + 2*x /          \     -1 + 2*x  /        \     -1 + 2*x  /|        |        |             2 ||  /        /        / /     2\ \\\|
                                   |       |        |     2*\1 + x /||    2*|3*x - -------------------------------------------- + ---------------------- - ----------------------|      2 |        \     -1 + 2*x  /|  |       2| 3      |-\1 + x / ||||
                                   |       |      2*|-1 + ----------||      |                              2                                    2           /     2\ /        2\ |   3*x *|3*x - -------------------| *|1 + cot |x  + log|----------||||
  /        /        / /     2\ \\\ |       |        |             2 ||      |                         1 + x                             /     2\            \1 + x /*\-1 + 2*x / |        |                  2      |  |        |        |        2 ||||
  |       2| 3      |-\1 + x / ||| |     2 |        \     -1 + 2*x  /|      \                                                           \1 + x /                                 /        \             1 + x       /  \        \        \-1 + 2*x  ///|
2*|1 + cot |x  + log|----------|||*|- 2*x *|3*x - -------------------|  + -------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------|
  |        |        |        2 ||| |       |                  2      |                                              /        / /     2\ \\                                                                   /        / /     2\ \\                    |
  \        \        \-1 + 2*x  /// |       \             1 + x       /                                              | 3      |-\1 + x / ||                                                                  2| 3      |-\1 + x / ||                    |
                                   |                                                                             cot|x  + log|----------||                                                               cot |x  + log|----------||                    |
                                   |                                                                                |        |        2 ||                                                                   |        |        2 ||                    |
                                   \                                                                                \        \-1 + 2*x  //                                                                   \        \-1 + 2*x  //                    /
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                                                                                                                   /        / /     2\ \\                                                                                                               
                                                                                                                  2| 3      |-\1 + x / ||                                                                                                               
                                                                                                               cot |x  + log|----------||                                                                                                               
                                                                                                                   |        |        2 ||                                                                                                               
                                                                                                                   \        \-1 + 2*x  //
2(cot⁡2(x3+log⁡(−x2+12x2−1))+1)(3x2(3x−2(2(x2+1)2x2−1−1)x2+1)2(cot⁡2(x3+log⁡(−x2+12x2−1))+1)cot⁡2(x3+log⁡(−x2+12x2−1))−2x2(3x−2(2(x2+1)2x2−1−1)x2+1)2+2(−4x2(2(x2+1)2x2−1−1)(x2+1)(2x2−1)+2x2(2(x2+1)2x2−1−1)(x2+1)2+3x−−16x2(x2+1)(2x2−1)2+8x22x2−1+2(x2+1)2x2−1−1x2+1)cot⁡(x3+log⁡(−x2+12x2−1)))cot⁡2(x3+log⁡(−x2+12x2−1))\frac{2 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{3 x^{2} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{2} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - 2 x^{2} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{2} + \frac{2 \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}
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Tercera derivada [src] 
                                   /                                 /          2       /     2\       2 /     2\\                                /          2       /     2\      2 /     2\\                               /          2       /     2\       2 /     2\\                                                                                                                                                                      /             /     2\         2         2 /     2\                                                  \                                                                                                                                          /             /     2\         2         2 /     2\                                                  \\
                                   |         /       /     2\\       |       8*x      2*\1 + x /   16*x *\1 + x /|       /       /     2\\        |       4*x      2*\1 + x /   8*x *\1 + x /|       /       /     2\\       |       8*x      2*\1 + x /   16*x *\1 + x /|         /       /     2\\                                                                       3                                        /        /       /     2\\\ |           2*\1 + x /      8*x      16*x *\1 + x /        /       /     2\\        /       /     2\\|                                                                     3                                        /        /       /     2\\\ |           2*\1 + x /      8*x      16*x *\1 + x /        /       /     2\\        /       /     2\\||
                                   |       3 |     2*\1 + x /|   4*x*|1 - --------- - ---------- + --------------|       |     2*\1 + x /|   24*x*|1 - --------- - ---------- + -------------|       |     2*\1 + x /|   8*x*|1 - --------- - ---------- + --------------|       3 |     2*\1 + x /|                                            /        /       /     2\\\                                         |        |     2*\1 + x /|| |      -1 + ---------- + --------- - --------------      2 |     2*\1 + x /|      2 |     2*\1 + x /||                                          /        /       /     2\\\                                         |        |     2*\1 + x /|| |      -1 + ---------- + --------- - --------------      2 |     2*\1 + x /|      2 |     2*\1 + x /|||
                                   |    8*x *|-1 + ----------|       |            2           2                2 |   2*x*|-1 + ----------|        |            2           2                2|   4*x*|-1 + ----------|       |            2           2                2 |   16*x *|-1 + ----------|                                            |        |     2*\1 + x /||                                         |      2*|-1 + ----------|| |                   2            2               2    2*x *|-1 + ----------|   4*x *|-1 + ----------||                                          |        |     2*\1 + x /||                                         |      2*|-1 + ----------|| |                   2            2               2    2*x *|-1 + ----------|   4*x *|-1 + ----------|||
                                   |         |             2 |       |    -1 + 2*x    -1 + 2*x      /        2\  |       |             2 |        |    -1 + 2*x    -1 + 2*x      /        2\ |       |             2 |       |    -1 + 2*x    -1 + 2*x      /        2\  |         |             2 |                                   3        |      2*|-1 + ----------||                                         |        |             2 || |           -1 + 2*x     -1 + 2*x     /        2\          |             2 |        |             2 ||                                        2 |      2*|-1 + ----------||        /        /        / /     2\ \\\ |        |             2 || |           -1 + 2*x     -1 + 2*x     /        2\          |             2 |        |             2 |||
                                   |         \     -1 + 2*x  /       \                              \-1 + 2*x /  /       \     -1 + 2*x  /        \                              \-1 + 2*x / /       \     -1 + 2*x  /       \                              \-1 + 2*x /  /         \     -1 + 2*x  /        /        /       /     2\\\         |        |             2 ||  /        /        / /     2\ \\\       |        \     -1 + 2*x  /| |                                     \-1 + 2*x /          \     -1 + 2*x  /        \     -1 + 2*x  /|        /        /        / /     2\ \\\  |        |             2 ||        |       2| 3      |-\1 + x / ||| |        \     -1 + 2*x  /| |                                     \-1 + 2*x /          \     -1 + 2*x  /        \     -1 + 2*x  /||
                                   |3 - ---------------------- - ------------------------------------------------- + --------------------- - ------------------------------------------------- - --------------------- + ------------------------------------------------- + -----------------------        |        |     2*\1 + x /||       3 |        \     -1 + 2*x  /|  |       2| 3      |-\1 + x / |||   6*x*|3*x - -------------------|*|3*x - -------------------------------------------- + ---------------------- - ----------------------|      3 |       2| 3      |-\1 + x / |||  |        \     -1 + 2*x  /|    9*x*|1 + cot |x  + log|----------|||*|3*x - -------------------|*|3*x - -------------------------------------------- + ---------------------- - ----------------------||
                                   |                  3                                      2                                     2                        /     2\ /        2\                  /     2\ /        2\                  /     2\ /        2\                          2                     |      2*|-1 + ----------||    8*x *|3*x - -------------------| *|1 + cot |x  + log|----------|||       |                  2      | |                              2                                    2           /     2\ /        2\ |   6*x *|1 + cot |x  + log|----------||| *|3*x - -------------------|        |        |        |        2 ||| |                  2      | |                              2                                    2           /     2\ /        2\ ||
  /        /        / /     2\ \\\ |          /     2\                               /     2\                              /     2\                         \1 + x /*\-1 + 2*x /                  \1 + x /*\-1 + 2*x /                  \1 + x /*\-1 + 2*x /                  /     2\  /        2\         |        |             2 ||         |                  2      |  |        |        |        2 |||       \             1 + x       / |                         1 + x                             /     2\            \1 + x /*\-1 + 2*x / |        |        |        |        2 |||  |                  2      |        \        \        \-1 + 2*x  /// \             1 + x       / |                         1 + x                             /     2\            \1 + x /*\-1 + 2*x / ||
  |       2| 3      |-\1 + x / ||| |          \1 + x /                               \1 + x /                              \1 + x /                                                                                                                                           \1 + x / *\-1 + 2*x /       3 |        \     -1 + 2*x  /|         \             1 + x       /  \        \        \-1 + 2*x  ///                                   \                                                           \1 + x /                                 /        \        \        \-1 + 2*x  ///  \             1 + x       /                                                                     \                                                           \1 + x /                                 /|
4*|1 + cot |x  + log|----------|||*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + 2*x *|3*x - -------------------|  - ------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------|
  |        |        |        2 ||| |                                                                                                                       /        / /     2\ \\                                                                                                                           |                  2      |                            /        / /     2\ \\                                                                                /        / /     2\ \\                                                                                   /        / /     2\ \\                                                                                                  /        / /     2\ \\                                                                      |
  \        \        \-1 + 2*x  /// |                                                                                                                      2| 3      |-\1 + x / ||                                                                                                                           \             1 + x       /                           2| 3      |-\1 + x / ||                                                                                | 3      |-\1 + x / ||                                                                                  4| 3      |-\1 + x / ||                                                                                                 3| 3      |-\1 + x / ||                                                                      |
                                   |                                                                                                                   cot |x  + log|----------||                                                                                                                                                                              cot |x  + log|----------||                                                                             cot|x  + log|----------||                                                                               cot |x  + log|----------||                                                                                              cot |x  + log|----------||                                                                      |
                                   |                                                                                                                       |        |        2 ||                                                                                                                                                                                  |        |        2 ||                                                                                |        |        2 ||                                                                                   |        |        2 ||                                                                                                  |        |        2 ||                                                                      |
                                   \                                                                                                                       \        \-1 + 2*x  //                                                                                                                                                                                  \        \-1 + 2*x  //                                                                                \        \-1 + 2*x  //                                                                                   \        \-1 + 2*x  //                                                                                                  \        \-1 + 2*x  //                                                                      /
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                                                                                                                                                                                                                                                                                                                                                                                          | 3      |-\1 + x / ||                                                                                                                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                       cot|x  + log|----------||                                                                                                                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                          |        |        2 ||                                                                                                                                                                                                                                                                                                                                                                                       
                                                                                                                                                                                                                                                                                                                                                                                          \        \-1 + 2*x  //
4(cot⁡2(x3+log⁡(−x2+12x2−1))+1)(6x3(3x−2(2(x2+1)2x2−1−1)x2+1)3(cot⁡2(x3+log⁡(−x2+12x2−1))+1)2cot⁡4(x3+log⁡(−x2+12x2−1))−8x3(3x−2(2(x2+1)2x2−1−1)x2+1)3(cot⁡2(x3+log⁡(−x2+12x2−1))+1)cot⁡2(x3+log⁡(−x2+12x2−1))+2x3(3x−2(2(x2+1)2x2−1−1)x2+1)3+9x(3x−2(2(x2+1)2x2−1−1)x2+1)(cot⁡2(x3+log⁡(−x2+12x2−1))+1)(−4x2(2(x2+1)2x2−1−1)(x2+1)(2x2−1)+2x2(2(x2+1)2x2−1−1)(x2+1)2+3x−−16x2(x2+1)(2x2−1)2+8x22x2−1+2(x2+1)2x2−1−1x2+1)cot⁡3(x3+log⁡(−x2+12x2−1))−6x(3x−2(2(x2+1)2x2−1−1)x2+1)(−4x2(2(x2+1)2x2−1−1)(x2+1)(2x2−1)+2x2(2(x2+1)2x2−1−1)(x2+1)2+3x−−16x2(x2+1)(2x2−1)2+8x22x2−1+2(x2+1)2x2−1−1x2+1)cot⁡(x3+log⁡(−x2+12x2−1))+16x3(2(x2+1)2x2−1−1)(x2+1)2(2x2−1)−8x3(2(x2+1)2x2−1−1)(x2+1)3−4x(2(x2+1)2x2−1−1)(x2+1)(2x2−1)−24x(8x2(x2+1)(2x2−1)2−4x22x2−1−2(x2+1)2x2−1+1)(x2+1)(2x2−1)+8x(16x2(x2+1)(2x2−1)2−8x22x2−1−2(x2+1)2x2−1+1)(x2+1)(2x2−1)+2x(2(x2+1)2x2−1−1)(x2+1)2−4x(16x2(x2+1)(2x2−1)2−8x22x2−1−2(x2+1)2x2−1+1)(x2+1)2+3cot⁡2(x3+log⁡(−x2+12x2−1)))cot⁡(x3+log⁡(−x2+12x2−1))\frac{4 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{6 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)^{2}}{\cot^{4}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - \frac{8 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} + 2 x^{3} \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right)^{3} + \frac{9 x \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right) \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)} + 1\right) \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot^{3}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} - \frac{6 x \left(3 x - \frac{2 \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{x^{2} + 1}\right) \left(- \frac{4 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x^{2} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} + 3 x - \frac{- \frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} + \frac{8 x^{2}}{2 x^{2} - 1} + \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}} + \frac{\frac{16 x^{3} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2} \left(2 x^{2} - 1\right)} - \frac{8 x^{3} \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{3}} - \frac{4 x \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} - \frac{24 x \left(\frac{8 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{4 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{8 x \left(\frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{8 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right) \left(2 x^{2} - 1\right)} + \frac{2 x \left(\frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{4 x \left(\frac{16 x^{2} \left(x^{2} + 1\right)}{\left(2 x^{2} - 1\right)^{2}} - \frac{8 x^{2}}{2 x^{2} - 1} - \frac{2 \left(x^{2} + 1\right)}{2 x^{2} - 1} + 1\right)}{\left(x^{2} + 1\right)^{2}} + 3}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{2 x^{2} - 1} \right)} \right)}}
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Gráfico
Derivada de (ctg(x^3+(ln((x^2+1)/(1-2x^2)))))^(-2)
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