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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
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    /        / 2    \\
   2| 3      |x  + 1||
cot |x  + log|------||
    |        |     2||
    \        \1 - x //
1cot⁡2(x3+log⁡(x2+11−x2))\frac{1}{\cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)}} 
cot(x^3 + log((x^2 + 1)/(1 - x^2)))^(-2)
Gráfica
02468-8-6-4-2-1010-5000001000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                 /                /             / 2    \\\
                                 |       /     2\ | 2*x     2*x*\x  + 1/||
                                 |       \1 - x /*|------ + ------------||
                                 |                |     2            2  ||
   /         /        / 2    \\\ |                |1 - x     /     2\   ||
   |        2| 3      |x  + 1||| |   2            \          \1 - x /   /|
-2*|-1 - cot |x  + log|------|||*|3*x  + --------------------------------|
   |         |        |     2||| |                     2                 |
   \         \        \1 - x /// \                    x  + 1             /
--------------------------------------------------------------------------
                              /        / 2    \\                          
                             3| 3      |x  + 1||                          
                          cot |x  + log|------||                          
                              |        |     2||                          
                              \        \1 - x //
−2(3x2+(1−x2)(2x1−x2+2x(x2+1)(1−x2)2)x2+1)(−cot⁡2(x3+log⁡(x2+11−x2))−1)cot⁡3(x3+log⁡(x2+11−x2))- \frac{2 \left(3 x^{2} + \frac{\left(1 - x^{2}\right) \left(\frac{2 x}{1 - x^{2}} + \frac{2 x \left(x^{2} + 1\right)}{\left(1 - x^{2}\right)^{2}}\right)}{x^{2} + 1}\right) \left(- \cot^{2}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)} - 1\right)}{\cot^{3}{\left(x^{3} + \log{\left(\frac{x^{2} + 1}{1 - x^{2}} \right)} \right)}}
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Segunda derivada [src] 
                                   /                                    /                 2        2       2 /     2\                                            \                                                                 \
                                   |                                    |            1 + x      4*x     4*x *\1 + x /        /           2\        /           2\|                               2                                 |
                                   |                                    |      -1 + ------- + ------- - -------------      2 |      1 + x |      2 |      1 + x ||        /        /          2\\                                  |
                                   |                                    |                 2         2              2    2*x *|-1 + -------|   2*x *|-1 + -------||        |        |     1 + x ||                                  |
                                   |                              2     |           -1 + x    -1 + x      /      2\          |           2|        |           2||        |      2*|1 - -------||                                  |
                                   |       /        /          2\\      |                                 \-1 + x /          \     -1 + x /        \     -1 + x /|        |        |          2||  /        /        / /     2\ \\\|
                                   |       |        |     1 + x ||    2*|3*x - -------------------------------------- + ------------------- - -------------------|      2 |        \    -1 + 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 + x /|        |                2    |  |        |        |       2  ||||
  |       2| 3      |-\1 + x / ||| |     2 |        \    -1 + x /|      \                                                    \1 + x /                            /        \           1 + x     /  \        \        \ -1 + x   ///|
2*|1 + cot |x  + log|----------|||*|- 2*x *|3*x + ---------------|  + -------------------------------------------------------------------------------------------- + --------------------------------------------------------------|
  |        |        |       2  ||| |       |                2    |                                        /        / /     2\ \\                                                           /        / /     2\ \\                  |
  \        \        \ -1 + x   /// |       \           1 + x     /                                        | 3      |-\1 + x / ||                                                          2| 3      |-\1 + x / ||                  |
                                   |                                                                   cot|x  + log|----------||                                                       cot |x  + log|----------||                  |
                                   |                                                                      |        |       2  ||                                                           |        |       2  ||                  |
                                   \                                                                      \        \ -1 + x   //                                                           \        \ -1 + x   //                  /
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                                                                                                         /        / /     2\ \\                                                                                                     
                                                                                                        2| 3      |-\1 + x / ||                                                                                                     
                                                                                                     cot |x  + log|----------||                                                                                                     
                                                                                                         |        |       2  ||                                                                                                     
                                                                                                         \        \ -1 + x   //
2(cot⁡2(x3+log⁡(−x2+1x2−1))+1)(3x2(3x+2(1−x2+1x2−1)x2+1)2(cot⁡2(x3+log⁡(−x2+1x2−1))+1)cot⁡2(x3+log⁡(−x2+1x2−1))−2x2(3x+2(1−x2+1x2−1)x2+1)2+2(2x2(−1+x2+1x2−1)(x2+1)2−2x2(−1+x2+1x2−1)(x2−1)(x2+1)+3x−4x2x2−1−4x2(x2+1)(x2−1)2−1+x2+1x2−1x2+1)cot⁡(x3+log⁡(−x2+1x2−1)))cot⁡2(x3+log⁡(−x2+1x2−1))\frac{2 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{3 x^{2} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{2} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - 2 x^{2} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{2} + \frac{2 \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{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\       |      1 + x      4*x     4*x *\1 + x /|       /          2\        |      1 + x      2*x     2*x *\1 + x /|       /          2\        |      1 + x      4*x     4*x *\1 + x /|         /          2\                                                               3                                        /        /          2\\ |            1 + x      4*x     4*x *\1 + x /        /           2\        /           2\|                                                                 3                                        /        /          2\\ |            1 + x      4*x     4*x *\1 + x /        /           2\        /           2\||
                                   |          3 |     1 + x |   4*x*|-1 + ------- + ------- - -------------|       |     1 + x |   12*x*|-1 + ------- + ------- - -------------|       |     1 + x |    4*x*|-1 + ------- + ------- - -------------|       3 |     1 + x |                                        /        /          2\\                                         |        |     1 + x || |      -1 + ------- + ------- - -------------      2 |      1 + x |      2 |      1 + x ||                                          /        /          2\\                                         |        |     1 + x || |      -1 + ------- + ------- - -------------      2 |      1 + x |      2 |      1 + x |||
                                   |       8*x *|1 - -------|       |           2         2              2 |   2*x*|1 - -------|        |           2         2              2 |   2*x*|1 - -------|        |           2         2              2 |    8*x *|1 - -------|                                        |        |     1 + x ||                                         |      2*|1 - -------|| |                 2         2              2    2*x *|-1 + -------|   2*x *|-1 + -------||                                          |        |     1 + x ||                                         |      2*|1 - -------|| |                 2         2              2    2*x *|-1 + -------|   2*x *|-1 + -------|||
                                   |            |          2|       |     -1 + x    -1 + x      /      2\  |       |          2|        |     -1 + x    -1 + x      /      2\  |       |          2|        |     -1 + x    -1 + x      /      2\  |         |          2|                               3        |      2*|1 - -------||                                         |        |          2|| |           -1 + x    -1 + x      /      2\          |           2|        |           2||                                        2 |      2*|1 - -------||        /        /        / /     2\ \\\ |        |          2|| |           -1 + x    -1 + x      /      2\          |           2|        |           2|||
                                   |            \    -1 + x /       \                           \-1 + x /  /       \    -1 + x /        \                           \-1 + x /  /       \    -1 + x /        \                           \-1 + x /  /         \    -1 + x /        /        /          2\\         |        |          2||  /        /        / /     2\ \\\       |        \    -1 + x /| |                                 \-1 + x /          \     -1 + x /        \     -1 + x /|        /        /        / /     2\ \\\  |        |          2||        |       2| 3      |-\1 + x / ||| |        \    -1 + x /| |                                 \-1 + x /          \     -1 + x /        \     -1 + x /||
                                   |  -3 - ------------------ - -------------------------------------------- + ----------------- - --------------------------------------------- - ------------------ + -------------------------------------------- + -------------------        |        |     1 + x ||       3 |        \    -1 + x /|  |       2| 3      |-\1 + x / |||   6*x*|3*x + ---------------|*|3*x - -------------------------------------- + ------------------- - -------------------|      3 |       2| 3      |-\1 + x / |||  |        \    -1 + 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 + x /                \1 + x /*\-1 + x /                \1 + x /*\-1 + x /                /     2\  /      2\        |        |          2||         |                2    |  |        |        |       2  |||       \           1 + x     / |                      1 + x                         /     2\          \1 + x /*\-1 + x /|        |        |        |       2  |||  |                2    |        \        \        \ -1 + x   /// \           1 + x     / |                      1 + x                         /     2\          \1 + x /*\-1 + x /||
  |       2| 3      |-\1 + x / ||| |           \1 + x /                          \1 + x /                          \1 + x /                                                                                                                            \1 + x / *\-1 + x /      3 |        \    -1 + x /|         \           1 + x     /  \        \        \ -1 + x   ///                               \                                                    \1 + x /                            /        \        \        \ -1 + x   ///  \           1 + x     /                                                                 \                                                    \1 + x /                            /|
4*|1 + cot |x  + log|----------|||*|- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 2*x *|3*x + ---------------|  - -------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------|
  |        |        |       2  ||| |                                                                                                           /        / /     2\ \\                                                                                                             |                2    |                          /        / /     2\ \\                                                                      /        / /     2\ \\                                                                         /        / /     2\ \\                                                                                        /        / /     2\ \\                                                              |
  \        \        \ -1 + 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 + x   //                                                                                                                                                              \        \ -1 + x   //                                                                      \        \ -1 + x   //                                                                         \        \ -1 + x   //                                                                                        \        \ -1 + x   //                                                              /
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                                                                                                                                                                                                                                                                                                                                                       | 3      |-\1 + x / ||                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                    cot|x  + log|----------||                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                       |        |       2  ||                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                       \        \ -1 + x   //
4(cot⁡2(x3+log⁡(−x2+1x2−1))+1)(6x3(3x+2(1−x2+1x2−1)x2+1)3(cot⁡2(x3+log⁡(−x2+1x2−1))+1)2cot⁡4(x3+log⁡(−x2+1x2−1))−8x3(3x+2(1−x2+1x2−1)x2+1)3(cot⁡2(x3+log⁡(−x2+1x2−1))+1)cot⁡2(x3+log⁡(−x2+1x2−1))+2x3(3x+2(1−x2+1x2−1)x2+1)3+9x(3x+2(1−x2+1x2−1)x2+1)(cot⁡2(x3+log⁡(−x2+1x2−1))+1)(2x2(−1+x2+1x2−1)(x2+1)2−2x2(−1+x2+1x2−1)(x2−1)(x2+1)+3x−4x2x2−1−4x2(x2+1)(x2−1)2−1+x2+1x2−1x2+1)cot⁡3(x3+log⁡(−x2+1x2−1))−6x(3x+2(1−x2+1x2−1)x2+1)(2x2(−1+x2+1x2−1)(x2+1)2−2x2(−1+x2+1x2−1)(x2−1)(x2+1)+3x−4x2x2−1−4x2(x2+1)(x2−1)2−1+x2+1x2−1x2+1)cot⁡(x3+log⁡(−x2+1x2−1))−−8x3(1−x2+1x2−1)(x2+1)3+8x3(1−x2+1x2−1)(x2−1)(x2+1)2+2x(1−x2+1x2−1)(x2+1)2−2x(1−x2+1x2−1)(x2−1)(x2+1)−4x(4x2x2−1−4x2(x2+1)(x2−1)2−1+x2+1x2−1)(x2+1)2−12x(2x2x2−1−2x2(x2+1)(x2−1)2−1+x2+1x2−1)(x2−1)(x2+1)+4x(4x2x2−1−4x2(x2+1)(x2−1)2−1+x2+1x2−1)(x2−1)(x2+1)−3cot⁡2(x3+log⁡(−x2+1x2−1)))cot⁡(x3+log⁡(−x2+1x2−1))\frac{4 \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{6 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)^{2}}{\cot^{4}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{8 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right)}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} + 2 x^{3} \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right)^{3} + \frac{9 x \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right) \left(\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)} + 1\right) \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot^{3}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{6 x \left(3 x + \frac{2 \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{x^{2} + 1}\right) \left(\frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x^{2} \left(-1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + 3 x - \frac{\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}}{x^{2} + 1}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}} - \frac{- \frac{8 x^{3} \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{3}} + \frac{8 x^{3} \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)^{2}} + \frac{2 x \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{2 x \left(1 - \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} - \frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 x \left(\frac{2 x^{2}}{x^{2} - 1} - \frac{2 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} + \frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - \frac{4 x^{2} \left(x^{2} + 1\right)}{\left(x^{2} - 1\right)^{2}} - 1 + \frac{x^{2} + 1}{x^{2} - 1}\right)}{\left(x^{2} - 1\right) \left(x^{2} + 1\right)} - 3}{\cot^{2}{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}\right)}{\cot{\left(x^{3} + \log{\left(- \frac{x^{2} + 1}{x^{2} - 1} \right)} \right)}}
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Gráfico
Derivada de (ctg(x^3+(ln((x^2+1)/(1-x^2)))))^(-2)
    © Sr Examen – Калькулятор