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y=(3sqrt(1+x^2)+2tg^2x)^(xlnx)
Derivada de la función/ y=(3sqrt(1+x^2)+2tg^2x)^(xlnx)

Derivada de y=(3sqrt(1+x^2)+2tg^2x)^(xlnx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
                           x*log(x)
/     ________            \        
|    /      2         2   |        
\3*\/  1 + x   + 2*tan (x)/
(3x2+1+2tan⁡2(x))xlog⁡(x)\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{x \log{\left(x \right)}} 
(3*sqrt(1 + x^2) + 2*tan(x)^2)^(x*log(x))
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (xlog⁡(x))xlog⁡(x)(log⁡(xlog⁡(x))+1)\left(x \log{\left(x \right)}\right)^{x \log{\left(x \right)}} \left(\log{\left(x \log{\left(x \right)} \right)} + 1\right)

Respuesta:

(xlog⁡(x))xlog⁡(x)(log⁡(xlog⁡(x))+1)\left(x \log{\left(x \right)}\right)^{x \log{\left(x \right)}} \left(\log{\left(x \log{\left(x \right)} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-5e435e43
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                    /                                                /  /         2   \              3*x    \       \
                                    |                                              x*|2*\2 + 2*tan (x)/*tan(x) + -----------|*log(x)|
                           x*log(x) |                                                |                              ________|       |
/     ________            \         |                /     ________            \     |                             /      2 |       |
|    /      2         2   |         |                |    /      2         2   |     \                           \/  1 + x  /       |
\3*\/  1 + x   + 2*tan (x)/        *|(1 + log(x))*log\3*\/  1 + x   + 2*tan (x)/ + -------------------------------------------------|
                                    |                                                               ________                        |
                                    |                                                              /      2         2               |
                                    \                                                          3*\/  1 + x   + 2*tan (x)            /
(x(3xx2+1+2(2tan⁡2(x)+2)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+(log⁡(x)+1)log⁡(3x2+1+2tan⁡2(x)))(3x2+1+2tan⁡2(x))xlog⁡(x)\left(\frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 2 \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right) \log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}\right) \left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{x \log{\left(x \right)}}
Simplificar
Segunda derivada [src] 
                                    /                                                                                               2                                                                                                                                                                                   /                             2          2                             \                                                  2       \
                                    |/                                                /    3*x         /       2   \       \       \                                         3*x         /       2   \                       /    3*x         /       2   \       \   /    3*x         /       2   \       \            |     3          /       2   \        3*x            2    /       2   \|            /    3*x         /       2   \       \        |
                                    ||                                              x*|----------- + 4*\1 + tan (x)/*tan(x)|*log(x)|                                     ----------- + 4*\1 + tan (x)/*tan(x)   (1 + log(x))*|----------- + 4*\1 + tan (x)/*tan(x)|   |----------- + 4*\1 + tan (x)/*tan(x)|*log(x)   x*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|*log(x)   x*|----------- + 4*\1 + tan (x)/*tan(x)| *log(x)|
                           x*log(x) ||                                                |   ________                         |       |       /                 ________\      ________                                         |   ________                         |   |   ________                         |            |   ________                              3/2                          |            |   ________                         |        |
/                 ________\         ||                /                 ________\     |  /      2                          |       |       |     2          /      2 |     /      2                                          |  /      2                          |   |  /      2                          |            |  /      2                       /     2\                             |            |  /      2                          |        |
|     2          /      2 |         ||                |     2          /      2 |     \\/  1 + x                           /       |    log\2*tan (x) + 3*\/  1 + x  /   \/  1 + x                                           \\/  1 + x                           /   \\/  1 + x                           /            \\/  1 + x                        \1 + x /                             /            \\/  1 + x                           /        |
\2*tan (x) + 3*\/  1 + x  /        *||(1 + log(x))*log\2*tan (x) + 3*\/  1 + x  / + -----------------------------------------------|  + ------------------------------ + ------------------------------------ + --------------------------------------------------- + --------------------------------------------- + --------------------------------------------------------------------------------- - ------------------------------------------------|
                                    ||                                                                          ________           |                  x                                        ________                                       ________                                           ________                                                          ________                                                                    2          |
                                    ||                                                              2          /      2            |                                               2          /      2                            2          /      2                                2          /      2                                               2          /      2                                          /                 ________\           |
                                    |\                                                         2*tan (x) + 3*\/  1 + x             /                                          2*tan (x) + 3*\/  1 + x                        2*tan (x) + 3*\/  1 + x                            2*tan (x) + 3*\/  1 + x                                           2*tan (x) + 3*\/  1 + x                                           |     2          /      2 |           |
                                    \                                                                                                                                                                                                                                                                                                                                                                               \2*tan (x) + 3*\/  1 + x  /           /
(3x2+1+2tan⁡2(x))xlog⁡(x)(−x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))2log⁡(x)(3x2+1+2tan⁡2(x))2+x(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)log⁡(x)3x2+1+2tan⁡2(x)+(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))(log⁡(x)+1)3x2+1+2tan⁡2(x)+(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+3xx2+1+4(tan⁡2(x)+1)tan⁡(x)3x2+1+2tan⁡2(x)+(x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+(log⁡(x)+1)log⁡(3x2+1+2tan⁡2(x)))2+log⁡(3x2+1+2tan⁡2(x))x)\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{x \log{\left(x \right)}} \left(- \frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2} \log{\left(x \right)}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} + \frac{x \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\log{\left(x \right)} + 1\right)}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \left(\frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right) \log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}\right)^{2} + \frac{\log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}}{x}\right)
Simplificar
Tercera derivada [src] 
                                    /                                                                                               3                                                                            2     /                             2          2                             \                                                                                                     /                                                                                                                                                                                /                             2          2                             \                                                  2       \                /                             2          2                             \                                         2                                                        2            /                             2          2                             \                                                       /                       3                                                 2       \                                                    3                                                     /                             2          2                             \       \
                                    |/                                                /    3*x         /       2   \       \       \                                       /    3*x         /       2   \       \      |     3          /       2   \        3*x            2    /       2   \|     /                                                /    3*x         /       2   \       \       \ |                                     3*x         /       2   \                       /    3*x         /       2   \       \   /    3*x         /       2   \       \            |     3          /       2   \        3*x            2    /       2   \|            /    3*x         /       2   \       \        |                |     3          /       2   \        3*x            2    /       2   \|   /    3*x         /       2   \       \                   /    3*x         /       2   \       \             |     3          /       2   \        3*x            2    /       2   \|            /    3*x         /       2   \       \     |      9*x           9*x             3    /       2   \      /       2   \        |              /    3*x         /       2   \       \               /    3*x         /       2   \       \ |     3          /       2   \        3*x            2    /       2   \|       |
                                    ||                                              x*|----------- + 4*\1 + tan (x)/*tan(x)|*log(x)|                                     2*|----------- + 4*\1 + tan (x)/*tan(x)|    2*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|     |                                              x*|----------- + 4*\1 + tan (x)/*tan(x)|*log(x)| |                                 ----------- + 4*\1 + tan (x)/*tan(x)   (1 + log(x))*|----------- + 4*\1 + tan (x)/*tan(x)|   |----------- + 4*\1 + tan (x)/*tan(x)|*log(x)   x*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|*log(x)   x*|----------- + 4*\1 + tan (x)/*tan(x)| *log(x)|   (1 + log(x))*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|   |----------- + 4*\1 + tan (x)/*tan(x)| *(1 + log(x))   2*|----------- + 4*\1 + tan (x)/*tan(x)| *log(x)   2*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|*log(x)   3*|----------- + 4*\1 + tan (x)/*tan(x)|   x*|- ----------- + ----------- + 16*tan (x)*\1 + tan (x)/ + 32*\1 + tan (x)/ *tan(x)|*log(x)   2*x*|----------- + 4*\1 + tan (x)/*tan(x)| *log(x)   3*x*|----------- + 4*\1 + tan (x)/*tan(x)|*|----------- + 4*\1 + tan (x)/  - ----------- + 8*tan (x)*\1 + tan (x)/|*log(x)|
                           x*log(x) ||                                                |   ________                         |       |       /                 ________\     |   ________                         |      |   ________                              3/2                          |     |                                                |   ________                         |       | |   /                 ________\      ________                                         |   ________                         |   |   ________                         |            |   ________                              3/2                          |            |   ________                         |        |                |   ________                              3/2                          |   |   ________                         |                   |   ________                         |             |   ________                              3/2                          |            |   ________                         |     |          3/2           5/2                                                      |              |   ________                         |               |   ________                         | |   ________                              3/2                          |       |
/                 ________\         ||                /                 ________\     |  /      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          /      2 |         ||                |     2          /      2 |     \\/  1 + x                           /       |    log\2*tan (x) + 3*\/  1 + x  /     \\/  1 + x                           /      \\/  1 + x                        \1 + x /                             /     |                |     2          /      2 |     \\/  1 + x                           /       | |log\2*tan (x) + 3*\/  1 + x  /   \/  1 + x                                           \\/  1 + x                           /   \\/  1 + x                           /            \\/  1 + x                        \1 + x /                             /            \\/  1 + x                           /        |                \\/  1 + x                        \1 + x /                             /   \\/  1 + x                           /                   \\/  1 + x                           /             \\/  1 + x                        \1 + x /                             /            \\/  1 + x                           /     \  \1 + x /      \1 + x /                                                         /              \\/  1 + x                           /               \\/  1 + x                           / \\/  1 + x                        \1 + x /                             /       |
\2*tan (x) + 3*\/  1 + x  /        *||(1 + log(x))*log\2*tan (x) + 3*\/  1 + x  / + -----------------------------------------------|  - ------------------------------ - ----------------------------------------- + -------------------------------------------------------------------------- + 3*|(1 + log(x))*log\2*tan (x) + 3*\/  1 + x  / + -----------------------------------------------|*|------------------------------ + ------------------------------------ + --------------------------------------------------- + --------------------------------------------- + --------------------------------------------------------------------------------- - ------------------------------------------------| + ------------------------------------------------------------------------------------- - ---------------------------------------------------- - ------------------------------------------------ + --------------------------------------------------------------------------------- + ---------------------------------------- + -------------------------------------------------------------------------------------------- + -------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------|
                                    ||                                                                          ________           |                   2                                                   2                                                  ________                              |                                                                          ________           | |              x                                        ________                                       ________                                           ________                                                          ________                                                                    2          |                                                  ________                                                                        2                                                    2                                                          ________                                      /                 ________\                                                           ________                                                                           3                                                                                        2                                               |
                                    ||                                                              2          /      2            |                  x                         /                 ________\                                       2          /      2                               |                                                              2          /      2            | |                                           2          /      2                            2          /      2                                2          /      2                                               2          /      2                                          /                 ________\           |                                      2          /      2                                              /                 ________\                          /                 ________\                                               2          /      2                                       |     2          /      2 |                                               2          /      2                                                 /                 ________\                                                              /                 ________\                                                |
                                    |\                                                         2*tan (x) + 3*\/  1 + x             /                                            |     2          /      2 |                                  2*tan (x) + 3*\/  1 + x                                \                                                         2*tan (x) + 3*\/  1 + x             / |                                      2*tan (x) + 3*\/  1 + x                        2*tan (x) + 3*\/  1 + x                            2*tan (x) + 3*\/  1 + x                                           2*tan (x) + 3*\/  1 + x                                           |     2          /      2 |           |                                 2*tan (x) + 3*\/  1 + x                                               |     2          /      2 |                          |     2          /      2 |                                          2*tan (x) + 3*\/  1 + x                                      x*\2*tan (x) + 3*\/  1 + x  /                                          2*tan (x) + 3*\/  1 + x                                                  |     2          /      2 |                                                              |     2          /      2 |                                                |
                                    \                                                                                                                                           \2*tan (x) + 3*\/  1 + x  /                                                                                                                                                                                         \                                                                                                                                                                                                                                                                            \2*tan (x) + 3*\/  1 + x  /           /                                                                                                       \2*tan (x) + 3*\/  1 + x  /                          \2*tan (x) + 3*\/  1 + x  /                                                                                                                                                                                                                                                       \2*tan (x) + 3*\/  1 + x  /                                                              \2*tan (x) + 3*\/  1 + x  /                                                /
(3x2+1+2tan⁡2(x))xlog⁡(x)(2x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))3log⁡(x)(3x2+1+2tan⁡2(x))3−3x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)log⁡(x)(3x2+1+2tan⁡2(x))2+x(9x3(x2+1)52−9x(x2+1)32+32(tan⁡2(x)+1)2tan⁡(x)+16(tan⁡2(x)+1)tan⁡3(x))log⁡(x)3x2+1+2tan⁡2(x)−(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))2(log⁡(x)+1)(3x2+1+2tan⁡2(x))2−2(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))2log⁡(x)(3x2+1+2tan⁡2(x))2−2(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))2(3x2+1+2tan⁡2(x))2+(x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+(log⁡(x)+1)log⁡(3x2+1+2tan⁡2(x)))3+3(x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+(log⁡(x)+1)log⁡(3x2+1+2tan⁡2(x)))(−x(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))2log⁡(x)(3x2+1+2tan⁡2(x))2+x(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)log⁡(x)3x2+1+2tan⁡2(x)+(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))(log⁡(x)+1)3x2+1+2tan⁡2(x)+(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))log⁡(x)3x2+1+2tan⁡2(x)+3xx2+1+4(tan⁡2(x)+1)tan⁡(x)3x2+1+2tan⁡2(x)+log⁡(3x2+1+2tan⁡2(x))x)+(log⁡(x)+1)(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)3x2+1+2tan⁡2(x)+2(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)log⁡(x)3x2+1+2tan⁡2(x)+2(−3x2(x2+1)32+4(tan⁡2(x)+1)2+8(tan⁡2(x)+1)tan⁡2(x)+3x2+1)3x2+1+2tan⁡2(x)+3(3xx2+1+4(tan⁡2(x)+1)tan⁡(x))x(3x2+1+2tan⁡2(x))−log⁡(3x2+1+2tan⁡2(x))x2)\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{x \log{\left(x \right)}} \left(\frac{2 x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{3} \log{\left(x \right)}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{3}} - \frac{3 x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right) \log{\left(x \right)}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} + \frac{x \left(\frac{9 x^{3}}{\left(x^{2} + 1\right)^{\frac{5}{2}}} - \frac{9 x}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 32 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)} + 16 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} - \frac{\left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2} \left(\log{\left(x \right)} + 1\right)}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} - \frac{2 \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2} \log{\left(x \right)}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} - \frac{2 \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} + \left(\frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right) \log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \left(\log{\left(x \right)} + 1\right) \log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}\right) \left(- \frac{x \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2} \log{\left(x \right)}}{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)^{2}} + \frac{x \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\log{\left(x \right)} + 1\right)}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{\log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}}{x}\right) + \frac{\left(\log{\left(x \right)} + 1\right) \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right)}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{2 \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right) \log{\left(x \right)}}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{2 \left(- \frac{3 x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 8 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{3}{\sqrt{x^{2} + 1}}\right)}{3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}} + \frac{3 \left(\frac{3 x}{\sqrt{x^{2} + 1}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)}{x \left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)}\right)} - \frac{\log{\left(3 \sqrt{x^{2} + 1} + 2 \tan^{2}{\left(x \right)} \right)}}{x^{2}}\right)
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Gráfico
Derivada de y=(3sqrt(1+x^2)+2tg^2x)^(xlnx)
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