Sr Examen

Derivada de y=(tan3x)^x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
   x     
tan (3*x)
$$\tan^{x}{\left(3 x \right)}$$
tan(3*x)^x
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
          /  /         2     \                \
   x      |x*\3 + 3*tan (3*x)/                |
tan (3*x)*|------------------- + log(tan(3*x))|
          \      tan(3*x)                     /
$$\left(\frac{x \left(3 \tan^{2}{\left(3 x \right)} + 3\right)}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)}\right) \tan^{x}{\left(3 x \right)}$$
Segunda derivada [src]
          /                                     2                                                           \
          |/    /       2     \                \                      /                     /       2     \\|
   x      ||3*x*\1 + tan (3*x)/                |      /       2     \ |   2             3*x*\1 + tan (3*x)/||
tan (3*x)*||------------------- + log(tan(3*x))|  + 3*\1 + tan (3*x)/*|-------- + 6*x - -------------------||
          |\      tan(3*x)                     /                      |tan(3*x)                 2          ||
          \                                                           \                      tan (3*x)     //
$$\left(\left(\frac{3 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)}\right)^{2} + 3 \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(- \frac{3 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\tan^{2}{\left(3 x \right)}} + 6 x + \frac{2}{\tan{\left(3 x \right)}}\right)\right) \tan^{x}{\left(3 x \right)}$$
Tercera derivada [src]
          /                                          3                                    2                        2                                                                                                                        3                                 \
          |     /    /       2     \                \                      /       2     \          /       2     \                      /    /       2     \                \ /                     /       2     \\        /       2     \                                  |
   x      |     |3*x*\1 + tan (3*x)/                |          2        27*\1 + tan (3*x)/    108*x*\1 + tan (3*x)/      /       2     \ |3*x*\1 + tan (3*x)/                | |   2             3*x*\1 + tan (3*x)/|   54*x*\1 + tan (3*x)/          /       2     \         |
tan (3*x)*|54 + |------------------- + log(tan(3*x))|  + 54*tan (3*x) - ------------------- - ---------------------- + 9*\1 + tan (3*x)/*|------------------- + log(tan(3*x))|*|-------- + 6*x - -------------------| + --------------------- + 108*x*\1 + tan (3*x)/*tan(3*x)|
          |     \      tan(3*x)                     /                           2                    tan(3*x)                            \      tan(3*x)                     / |tan(3*x)                 2          |            3                                            |
          \                                                                  tan (3*x)                                                                                         \                      tan (3*x)     /         tan (3*x)                                       /
$$\left(\frac{54 x \left(\tan^{2}{\left(3 x \right)} + 1\right)^{3}}{\tan^{3}{\left(3 x \right)}} - \frac{108 x \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2}}{\tan{\left(3 x \right)}} + 108 x \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)} + \left(\frac{3 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)}\right)^{3} + 9 \left(\frac{3 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\tan{\left(3 x \right)}} + \log{\left(\tan{\left(3 x \right)} \right)}\right) \left(\tan^{2}{\left(3 x \right)} + 1\right) \left(- \frac{3 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\tan^{2}{\left(3 x \right)}} + 6 x + \frac{2}{\tan{\left(3 x \right)}}\right) - \frac{27 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2}}{\tan^{2}{\left(3 x \right)}} + 54 \tan^{2}{\left(3 x \right)} + 54\right) \tan^{x}{\left(3 x \right)}$$
Gráfico
Derivada de y=(tan3x)^x