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acot(e^(2*x))+log(sqrt(1+e^(2*x))/(e^(2*x)-1))
Derivada de la función/ acot(e^(2*x))+log(sqrt(1+e^(2*x))/(e^(2*x)-1))

Derivada de acot(e^(2*x))+log(sqrt(1+e^(2*x))/(e^(2*x)-1))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
                /   __________\
                |  /      2*x |
    / 2*x\      |\/  1 + E    |
acot\E   / + log|-------------|
                |    2*x      |
                \   E    - 1  /
log⁡(e2x+1e2x−1)+acot⁡(e2x)\log{\left(\frac{\sqrt{e^{2 x} + 1}}{e^{2 x} - 1} \right)} + \operatorname{acot}{\left(e^{2 x} \right)} 
acot(E^(2*x)) + log(sqrt(1 + E^(2*x))/(E^(2*x) - 1))
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                        /                                __________     \
                        |           2*x                 /      2*x   2*x|
             / 2*x    \ |          e                2*\/  1 + E    *e   |
             \E    - 1/*|------------------------ - --------------------|
                        |   __________                            2     |
      2*x               |  /      2*x  / 2*x    \       / 2*x    \      |
   2*e                  \\/  1 + E    *\E    - 1/       \E    - 1/      /
- -------- + ------------------------------------------------------------
       4*x                             __________                        
  1 + e                               /      2*x                         
                                    \/  1 + E
(e2x−1)(e2x(e2x−1)e2x+1−2e2x+1e2x(e2x−1)2)e2x+1−2e2xe4x+1\frac{\left(e^{2 x} - 1\right) \left(\frac{e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1} e^{2 x}}{\left(e^{2 x} - 1\right)^{2}}\right)}{\sqrt{e^{2 x} + 1}} - \frac{2 e^{2 x}}{e^{4 x} + 1}
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Segunda derivada [src] 
/                                                    __________        __________                                                  /                     __________\          /                     __________\     \     
|                                     2*x           /      2*x        /      2*x   2*x                2*x                          |                    /      2*x |          |                    /      2*x |     |     
|                     2              e          4*\/  1 + e       8*\/  1 + e    *e                4*e                             |      1         2*\/  1 + e    |  2*x     |      1         2*\/  1 + e    |  2*x|     
|             - ------------- + ------------- + --------------- - -------------------- + -------------------------                 |------------- - ---------------|*e      2*|------------- - ---------------|*e   |     
|                  __________             3/2            2*x                     2          __________                             |   __________            2*x   |          |   __________            2*x   |     |     
|                 /      2*x    /     2*x\         -1 + e             /      2*x\          /      2*x  /      2*x\         4*x     |  /      2*x       -1 + e      |          |  /      2*x       -1 + e      |     |     
|     4         \/  1 + e       \1 + e   /                            \-1 + e   /        \/  1 + e    *\-1 + e   /      8*e        \\/  1 + e                      /          \\/  1 + e                      /     |  2*x
|- -------- - ---------------------------------------------------------------------------------------------------- + ----------- - -------------------------------------- + ----------------------------------------|*e   
|       4*x                                                 __________                                                         2                         3/2                          __________                    |     
|  1 + e                                                   /      2*x                                                /     4*x\                /     2*x\                            /      2*x  /      2*x\        |     
\                                                        \/  1 + e                                                   \1 + e   /                \1 + e   /                          \/  1 + e    *\-1 + e   /        /
(−(1e2x+1−2e2x+1e2x−1)e2x(e2x+1)32+2(1e2x+1−2e2x+1e2x−1)e2x(e2x−1)e2x+1−4e4x+1+8e4x(e4x+1)2−−2e2x+1+e2x(e2x+1)32+4e2x+1e2x−1+4e2x(e2x−1)e2x+1−8e2x+1e2x(e2x−1)2e2x+1)e2x\left(- \frac{\left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{2 \left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{4}{e^{4 x} + 1} + \frac{8 e^{4 x}}{\left(e^{4 x} + 1\right)^{2}} - \frac{- \frac{2}{\sqrt{e^{2 x} + 1}} + \frac{e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{4 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1} + \frac{4 e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{8 \sqrt{e^{2 x} + 1} e^{2 x}}{\left(e^{2 x} - 1\right)^{2}}}{\sqrt{e^{2 x} + 1}}\right) e^{2 x}
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Tercera derivada [src] 
/                                  __________                                         __________                                                                                                   __________                                      /                     __________\          /                                       __________        __________                                 \          /                     __________\          /                     __________\          /                                       __________        __________                                 \          /                     __________\     \     
|                                 /      2*x           2*x             4*x           /      2*x   4*x                2*x                         4*x                         4*x                  /      2*x   2*x                                 |                    /      2*x |          |                        2*x           /      2*x        /      2*x   2*x                2*x         |          |                    /      2*x |          |                    /      2*x |          |                        2*x           /      2*x        /      2*x   2*x                2*x         |          |                    /      2*x |     |     
|                   4         8*\/  1 + e           6*e             3*e         48*\/  1 + e    *e               24*e                         6*e                        24*e                48*\/  1 + e    *e                                    |      1         2*\/  1 + e    |  2*x     |        2              e          4*\/  1 + e       8*\/  1 + e    *e                4*e            |  2*x     |      1         2*\/  1 + e    |  4*x     |      1         2*\/  1 + e    |  4*x     |        2              e          4*\/  1 + e       8*\/  1 + e    *e                4*e            |  2*x     |      1         2*\/  1 + e    |  2*x|     
|             ------------- - --------------- - ------------- + ------------- - --------------------- - ------------------------- + ------------------------- + -------------------------- + ---------------------                               2*|------------- - ---------------|*e      2*|- ------------- + ------------- + --------------- - -------------------- + -------------------------|*e      3*|------------- - ---------------|*e      4*|------------- - ---------------|*e      4*|- ------------- + ------------- + --------------- - -------------------- + -------------------------|*e      4*|------------- - ---------------|*e   |     
|                __________            2*x                3/2             5/2                   3          __________                         3/2                  __________            2                   2                                     |   __________            2*x   |          |     __________             3/2            2*x                     2          __________            |          |   __________            2*x   |          |   __________            2*x   |          |     __________             3/2            2*x                     2          __________            |          |   __________            2*x   |     |     
|               /      2*x       -1 + e         /     2*x\      /     2*x\           /      2*x\          /      2*x  /      2*x\   /     2*x\    /      2*x\     /      2*x  /      2*x\         /      2*x\              8*x           4*x       |  /      2*x       -1 + e      |          |    /      2*x    /     2*x\         -1 + e             /      2*x\          /      2*x  /      2*x\|          |  /      2*x       -1 + e      |          |  /      2*x       -1 + e      |          |    /      2*x    /     2*x\         -1 + e             /      2*x\          /      2*x  /      2*x\|          |  /      2*x       -1 + e      |     |     
|     8       \/  1 + e                         \1 + e   /      \1 + e   /           \-1 + e   /        \/  1 + e    *\-1 + e   /   \1 + e   /   *\-1 + e   /   \/  1 + e    *\-1 + e   /         \-1 + e   /          64*e          64*e          \\/  1 + e                      /          \  \/  1 + e       \1 + e   /                            \-1 + e   /        \/  1 + e    *\-1 + e   //          \\/  1 + e                      /          \\/  1 + e                      /          \  \/  1 + e       \1 + e   /                            \-1 + e   /        \/  1 + e    *\-1 + e   //          \\/  1 + e                      /     |  2*x
|- -------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------- + ----------- - ---------------------------------------- + ------------------------------------------------------------------------------------------------------------- + ---------------------------------------- - ---------------------------------------- - ------------------------------------------------------------------------------------------------------------- + ----------------------------------------|*e   
|       4*x                                                                                                 __________                                                                                                         3             2                          3/2                                                                           3/2                                                                          5/2                                  3/2                                                                    __________                                                                   __________                    |     
|  1 + e                                                                                                   /      2*x                                                                                                /     4*x\    /     4*x\                 /     2*x\                                                                    /     2*x\                                                                   /     2*x\                           /     2*x\    /      2*x\                                                       /      2*x  /      2*x\                                                      /      2*x  /      2*x\        |     
\                                                                                                        \/  1 + e                                                                                                   \1 + e   /    \1 + e   /                 \1 + e   /                                                                    \1 + e   /                                                                   \1 + e   /                           \1 + e   /   *\-1 + e   /                                                     \/  1 + e    *\-1 + e   /                                                    \/  1 + e    *\-1 + e   /        /
(−2(1e2x+1−2e2x+1e2x−1)e2x(e2x+1)32+3(1e2x+1−2e2x+1e2x−1)e4x(e2x+1)52+4(1e2x+1−2e2x+1e2x−1)e2x(e2x−1)e2x+1−4(1e2x+1−2e2x+1e2x−1)e4x(e2x−1)(e2x+1)32−8e4x+1+64e4x(e4x+1)2−64e8x(e4x+1)3+4e2x+1−6e2x(e2x+1)32+3e4x(e2x+1)52−8e2x+1e2x−1−24e2x(e2x−1)e2x+1+6e4x(e2x−1)(e2x+1)32+48e2x+1e2x(e2x−1)2+24e4x(e2x−1)2e2x+1−48e2x+1e4x(e2x−1)3e2x+1+2(−2e2x+1+e2x(e2x+1)32+4e2x+1e2x−1+4e2x(e2x−1)e2x+1−8e2x+1e2x(e2x−1)2)e2x(e2x+1)32−4(−2e2x+1+e2x(e2x+1)32+4e2x+1e2x−1+4e2x(e2x−1)e2x+1−8e2x+1e2x(e2x−1)2)e2x(e2x−1)e2x+1)e2x\left(- \frac{2 \left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{3 \left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{4 x}}{\left(e^{2 x} + 1\right)^{\frac{5}{2}}} + \frac{4 \left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{4 \left(\frac{1}{\sqrt{e^{2 x} + 1}} - \frac{2 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1}\right) e^{4 x}}{\left(e^{2 x} - 1\right) \left(e^{2 x} + 1\right)^{\frac{3}{2}}} - \frac{8}{e^{4 x} + 1} + \frac{64 e^{4 x}}{\left(e^{4 x} + 1\right)^{2}} - \frac{64 e^{8 x}}{\left(e^{4 x} + 1\right)^{3}} + \frac{\frac{4}{\sqrt{e^{2 x} + 1}} - \frac{6 e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{3 e^{4 x}}{\left(e^{2 x} + 1\right)^{\frac{5}{2}}} - \frac{8 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1} - \frac{24 e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} + \frac{6 e^{4 x}}{\left(e^{2 x} - 1\right) \left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{48 \sqrt{e^{2 x} + 1} e^{2 x}}{\left(e^{2 x} - 1\right)^{2}} + \frac{24 e^{4 x}}{\left(e^{2 x} - 1\right)^{2} \sqrt{e^{2 x} + 1}} - \frac{48 \sqrt{e^{2 x} + 1} e^{4 x}}{\left(e^{2 x} - 1\right)^{3}}}{\sqrt{e^{2 x} + 1}} + \frac{2 \left(- \frac{2}{\sqrt{e^{2 x} + 1}} + \frac{e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{4 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1} + \frac{4 e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{8 \sqrt{e^{2 x} + 1} e^{2 x}}{\left(e^{2 x} - 1\right)^{2}}\right) e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} - \frac{4 \left(- \frac{2}{\sqrt{e^{2 x} + 1}} + \frac{e^{2 x}}{\left(e^{2 x} + 1\right)^{\frac{3}{2}}} + \frac{4 \sqrt{e^{2 x} + 1}}{e^{2 x} - 1} + \frac{4 e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}} - \frac{8 \sqrt{e^{2 x} + 1} e^{2 x}}{\left(e^{2 x} - 1\right)^{2}}\right) e^{2 x}}{\left(e^{2 x} - 1\right) \sqrt{e^{2 x} + 1}}\right) e^{2 x}
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Gráfico
Derivada de acot(e^(2*x))+log(sqrt(1+e^(2*x))/(e^(2*x)-1))
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