Sr Examen

Otras calculadoras


y=(tg2x)^ctgx/2

Derivada de y=(tg2x)^ctgx/2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   cot(x)     
tan      (2*x)
--------------
      2       
$$\frac{\tan^{\cot{\left(x \right)}}{\left(2 x \right)}}{2}$$
tan(2*x)^cot(x)/2
Solución detallada
  1. La derivada del producto de una constante por función es igual al producto de esta constante por la derivada de esta función.

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

      Perola derivada

    Entonces, como resultado:


Respuesta:

Gráfica
Primera derivada [src]
               /                               /         2     \       \
   cot(x)      |/        2   \                 \2 + 2*tan (2*x)/*cot(x)|
tan      (2*x)*|\-1 - cot (x)/*log(tan(2*x)) + ------------------------|
               \                                       tan(2*x)        /
------------------------------------------------------------------------
                                   2                                    
$$\frac{\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cot{\left(x \right)}}{\tan{\left(2 x \right)}} + \left(- \cot^{2}{\left(x \right)} - 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \tan^{\cot{\left(x \right)}}{\left(2 x \right)}}{2}$$
Segunda derivada [src]
               /                                                          2                                               2                                                                                \
               |/                                  /       2     \       \                                 /       2     \             /       2   \ /       2     \                                       |
   cot(x)      ||  /       2   \                 2*\1 + tan (2*x)/*cot(x)|      /       2     \          4*\1 + tan (2*x)/ *cot(x)   4*\1 + cot (x)/*\1 + tan (2*x)/     /       2   \                     |
tan      (2*x)*||- \1 + cot (x)/*log(tan(2*x)) + ------------------------|  + 8*\1 + tan (2*x)/*cot(x) - ------------------------- - ------------------------------- + 2*\1 + cot (x)/*cot(x)*log(tan(2*x))|
               |\                                        tan(2*x)        /                                          2                            tan(2*x)                                                  |
               \                                                                                                 tan (2*x)                                                                                 /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                     2                                                                                                      
$$\frac{\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{2} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(x \right)} + 2 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(x \right)}\right) \tan^{\cot{\left(x \right)}}{\left(2 x \right)}}{2}$$
Tercera derivada [src]
               /                                                          3                                                                                                   /                                                                                   2                                         \                                                      2                                                                    2                                   3                                                                                      \
               |/                                  /       2     \       \                                         /                                  /       2     \       \ |                                                                    /       2     \             /       2   \ /       2     \|                  2                    /       2     \                                                      /       2     \  /       2   \      /       2     \                                                   /       2   \ /       2     \       |
   cot(x)      ||  /       2   \                 2*\1 + tan (2*x)/*cot(x)|       /       2   \ /       2     \     |  /       2   \                 2*\1 + tan (2*x)/*cot(x)| |    /       2     \          /       2   \                        2*\1 + tan (2*x)/ *cot(x)   2*\1 + cot (x)/*\1 + tan (2*x)/|     /       2   \                  32*\1 + tan (2*x)/ *cot(x)        2    /       2   \                 12*\1 + tan (2*x)/ *\1 + cot (x)/   16*\1 + tan (2*x)/ *cot(x)      /       2     \                   12*\1 + cot (x)/*\1 + tan (2*x)/*cot(x)|
tan      (2*x)*||- \1 + cot (x)/*log(tan(2*x)) + ------------------------|  - 24*\1 + cot (x)/*\1 + tan (2*x)/ - 6*|- \1 + cot (x)/*log(tan(2*x)) + ------------------------|*|- 4*\1 + tan (2*x)/*cot(x) - \1 + cot (x)/*cot(x)*log(tan(2*x)) + ------------------------- + -------------------------------| - 2*\1 + cot (x)/ *log(tan(2*x)) - -------------------------- - 4*cot (x)*\1 + cot (x)/*log(tan(2*x)) + --------------------------------- + -------------------------- + 32*\1 + tan (2*x)/*cot(x)*tan(2*x) + ---------------------------------------|
               |\                                        tan(2*x)        /                                         \                                        tan(2*x)        / |                                                                             2                            tan(2*x)           |                                             tan(2*x)                                                                   2                               3                                                                      tan(2*x)               |
               \                                                                                                                                                              \                                                                          tan (2*x)                                          /                                                                                                                     tan (2*x)                       tan (2*x)                                                                                        /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                 2                                                                                                                                                                                                                                                                                  
$$\frac{\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right)^{3} - 6 \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(2 x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)}\right) \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} + \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan{\left(2 x \right)}} - 4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cot{\left(x \right)} - \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot{\left(x \right)}\right) + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \cot{\left(x \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \left(\cot^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cot{\left(x \right)}}{\tan{\left(2 x \right)}} - 24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) + \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\tan{\left(2 x \right)}} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)} \cot{\left(x \right)} - 2 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\tan{\left(2 x \right)} \right)} - 4 \left(\cot^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(2 x \right)} \right)} \cot^{2}{\left(x \right)}\right) \tan^{\cot{\left(x \right)}}{\left(2 x \right)}}{2}$$
Gráfico
Derivada de y=(tg2x)^ctgx/2