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y=(tg(2x))^(ctg(x/2))

Derivada de y=(tg(2x))^(ctg(x/2))

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

Gráfico:

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Solución

Ha introducido [src]
             /x\
          cot|-|
             \2/
(tan(2*x))      
$$\tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
tan(2*x)^cot(x/2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
             /x\ //         2/x\\                 /         2     \    /x\\
          cot|-| ||      cot |-||                 \2 + 2*tan (2*x)/*cot|-||
             \2/ ||  1       \2/|                                      \2/|
(tan(2*x))      *||- - - -------|*log(tan(2*x)) + ------------------------|
                 \\  2      2   /                         tan(2*x)        /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} + \left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)}}{2} - \frac{1}{2}\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Segunda derivada [src]
                 /                                                          2                                                                                                                              \
                 |/                                  /       2     \    /x\\                                                                                                                               |
                 ||                                4*\1 + tan (2*x)/*cot|-||                                                                                     2                                         |
             /x\ ||  /       2/x\\                                      \2/|                               /       2/x\\    /x\                   /       2     \     /x\     /       2/x\\ /       2     \|
          cot|-| ||- |1 + cot |-||*log(tan(2*x)) + ------------------------|                               |1 + cot |-||*cot|-|*log(tan(2*x))   4*\1 + tan (2*x)/ *cot|-|   2*|1 + cot |-||*\1 + tan (2*x)/|
             \2/ |\  \        \2//                         tan(2*x)        /      /       2     \    /x\   \        \2//    \2/                                       \2/     \        \2//                |
(tan(2*x))      *|----------------------------------------------------------- + 8*\1 + tan (2*x)/*cot|-| + ---------------------------------- - ------------------------- - -------------------------------|
                 |                             4                                                     \2/                   2                               2                            tan(2*x)           |
                 \                                                                                                                                      tan (2*x)                                          /
$$\left(\frac{\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{2}}{4} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)} + \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(\frac{x}{2} \right)}}{2}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Tercera derivada [src]
                 /                                                                                                                                                              /                                                                                                                      2       \                                                                                                                                                                                                                                                \
                 |                                                          3                                        /                                  /       2     \    /x\\ |                                                                     /       2/x\\ /       2     \     /       2     \     /x\|                                                                                                                                                                                                                                                |
                 |/                                  /       2     \    /x\\                                         |                                4*\1 + tan (2*x)/*cot|-|| |                                                                   4*|1 + cot |-||*\1 + tan (2*x)/   8*\1 + tan (2*x)/ *cot|-||                                                                                                                                                                                                                                                |
                 ||                                4*\1 + tan (2*x)/*cot|-||                                         |  /       2/x\\                                      \2/| |     /       2     \    /x\   /       2/x\\    /x\                   \        \2//                                         \2/|                2                                   2                           2                                   3                                                                                                                           |
             /x\ ||  /       2/x\\                                      \2/|                                       3*|- |1 + cot |-||*log(tan(2*x)) + ------------------------|*|- 16*\1 + tan (2*x)/*cot|-| - |1 + cot |-||*cot|-|*log(tan(2*x)) + ------------------------------- + -------------------------|   /       2/x\\                     /       2     \     /x\     /       2     \  /       2/x\\      /       2     \     /x\                                           2/x\ /       2/x\\                   /       2/x\\ /       2     \    /x\|
          cot|-| ||- |1 + cot |-||*log(tan(2*x)) + ------------------------|                                         \  \        \2//                         tan(2*x)        / |                        \2/   \        \2//    \2/                             tan(2*x)                         2             |   |1 + cot |-|| *log(tan(2*x))   32*\1 + tan (2*x)/ *cot|-|   6*\1 + tan (2*x)/ *|1 + cot |-||   16*\1 + tan (2*x)/ *cot|-|                                        cot |-|*|1 + cot |-||*log(tan(2*x))   3*|1 + cot |-||*\1 + tan (2*x)/*cot|-||
             \2/ |\  \        \2//                         tan(2*x)        /       /       2/x\\ /       2     \                                                                \                                                                                                             tan (2*x)        /   \        \2//                                         \2/                      \        \2//                          \2/      /       2     \    /x\                \2/ \        \2//                   \        \2//                    \2/|
(tan(2*x))      *|----------------------------------------------------------- - 12*|1 + cot |-||*\1 + tan (2*x)/ - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------- - -------------------------- + -------------------------------- + -------------------------- + 32*\1 + tan (2*x)/*cot|-|*tan(2*x) - ----------------------------------- + --------------------------------------|
                 |                             8                                   \        \2//                                                                                                                 4                                                                                                              4                          tan(2*x)                          2                               3                                       \2/                             2                                   tan(2*x)               |
                 \                                                                                                                                                                                                                                                                                                                                                                        tan (2*x)                       tan (2*x)                                                                                                                             /
$$\left(\frac{\left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{3}}{8} - \frac{3 \left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \left(\frac{8 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(2 x \right)}} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan{\left(2 x \right)}} - 16 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(\frac{x}{2} \right)} - \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(\frac{x}{2} \right)}\right)}{4} + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \cot{\left(\frac{x}{2} \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)}{\tan^{2}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} - 12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) + \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \cot{\left(\frac{x}{2} \right)}}{\tan{\left(2 x \right)}} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \cot{\left(\frac{x}{2} \right)} - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \log{\left(\tan{\left(2 x \right)} \right)}}{4} - \frac{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot^{2}{\left(\frac{x}{2} \right)}}{2}\right) \tan^{\cot{\left(\frac{x}{2} \right)}}{\left(2 x \right)}$$
Gráfico
Derivada de y=(tg(2x))^(ctg(x/2))