Derivada de y=3^x^2^tgx

Ha introducido [src]

 / / tan(x)\\
 | \2      /|
 \x         /
3

3^{x^{2^{\tan{\left(x \right)}}}}

3^(x^(2^tan(x)))

Solución detallada

Sustituimos $u = x^{2^{\tan{\left(x \right)}}}$ .
$\frac{d}{d u} 3^{u} = 3^{u} \log{\left(3 \right)}$
Luego se aplica una cadena de reglas. Multiplicamos por $\frac{d}{d x} x^{2^{\tan{\left(x \right)}}}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $2^{2^{\tan{\left(x \right)}} \tan{\left(x \right)}} \left(\log{\left(2^{\tan{\left(x \right)}} \right)} + 1\right)$
Como resultado de la secuencia de reglas:

$2^{2^{\tan{\left(x \right)}} \tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} \left(\log{\left(2^{\tan{\left(x \right)}} \right)} + 1\right) \log{\left(3 \right)}$
Simplificamos:

$2^{2^{\tan{\left(x \right)}} \tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} \left(\log{\left(2 \right)} \tan{\left(x \right)} + 1\right) \log{\left(3 \right)}$

Respuesta:

$2^{2^{\tan{\left(x \right)}} \tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} \left(\log{\left(2 \right)} \tan{\left(x \right)} + 1\right) \log{\left(3 \right)}$

Primera derivada [src]

 / / tan(x)\\                                                                  
 | \2      /|  / tan(x)\ / tan(x)                                      \       
 \x         /  \2      / |2          tan(x) /       2   \              |       
3            *x         *|------- + 2      *\1 + tan (x)/*log(2)*log(x)|*log(3)
                         \   x                                         /

3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{\tan{\left(x \right)}} \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{2^{\tan{\left(x \right)}}}{x}\right) \log{\left(3 \right)}

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Segunda derivada [src]

         / / tan(x)\\                                                                                                                                                                                                                                     
         | \2      /|  / tan(x)\ /                                                2                2                    /       2   \                   / tan(x)\                                  2                                              \       
 tan(x)  \x         /  \2      / |  1     tan(x) /1   /       2   \              \    /       2   \     2             2*\1 + tan (x)/*log(2)    tan(x)  \2      / /1   /       2   \              \             /       2   \                     |       
2      *3            *x         *|- -- + 2      *|- + \1 + tan (x)/*log(2)*log(x)|  + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2      *x         *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3)
                                 |   2           \x                              /                                              x                                 \x                              /                                               |       
                                 \  x                                                                                                                                                                                                             /

2^{\tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{\tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} \log{\left(3 \right)} + 2^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(3 \right)}

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Tercera derivada [src]

         / / tan(x)\\            /                                                                                                                                                                                                                                                                                                                  2                                                                                                                                                                                                                                                                                                                                                                                                                                     \       
         | \2      /|  / tan(x)\ |                                                3                3                    /       2   \                         2                                                             /                    2                    /       2   \                                              \     /       2   \     2                    tan(x)                                  3                        / tan(x)\                                  3                                                    /       2   \                                2                                    / tan(x)\                                   /                    2                    /       2   \                                              \       |       
 tan(x)  \x         /  \2      / |2     2*tan(x) /1   /       2   \              \    /       2   \     3             3*\1 + tan (x)/*log(2)     /       2   \                     tan(x) /1   /       2   \              \ |  1    /       2   \     2             2*\1 + tan (x)/*log(2)     /       2   \                     |   3*\1 + tan (x)/ *log (2)    2*tan(x)  2*2       /1   /       2   \              \     2         2*tan(x)  \2      / /1   /       2   \              \                2    /       2   \                 6*\1 + tan (x)/*log(2)*tan(x)     /       2   \     2                       tan(x)  \2      / /1   /       2   \              \ |  1    /       2   \     2             2*\1 + tan (x)/*log(2)     /       2   \                     |       |       
2      *3            *x         *|-- + 2        *|- + \1 + tan (x)/*log(2)*log(x)|  + \1 + tan (x)/ *log (2)*log(x) - ---------------------- + 2*\1 + tan (x)/ *log(2)*log(x) + 3*2      *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)| + ------------------------ + 2        *x         *|- + \1 + tan (x)/*log(2)*log(x)| *log (3) + 3*2        *x         *|- + \1 + tan (x)/*log(2)*log(x)| *log(3) + 4*tan (x)*\1 + tan (x)/*log(2)*log(x) + ----------------------------- + 6*\1 + tan (x)/ *log (2)*log(x)*tan(x) + 3*2      *x         *|- + \1 + tan (x)/*log(2)*log(x)|*|- -- + \1 + tan (x)/ *log (2)*log(x) + ---------------------- + 2*\1 + tan (x)/*log(2)*log(x)*tan(x)|*log(3)|*log(3)
                                 | 3             \x                              /                                               2                                                        \x                              / |   2                                             x                                                  |              x                                    \x                              /                                   \x                              /                                                                 x                                                                               \x                              / |   2                                             x                                                  |       |       
                                 \x                                                                                             x                                                                                           \  x                                                                                                 /                                                                                                                                                                                                                                                                                                                                           \  x                                                                                                 /       /

2^{\tan{\left(x \right)}} 3^{x^{2^{\tan{\left(x \right)}}}} x^{2^{\tan{\left(x \right)}}} \left(2^{2 \tan{\left(x \right)}} x^{2 \cdot 2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(3 \right)}^{2} + 3 \cdot 2^{2 \tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} \log{\left(3 \right)} + 2^{2 \tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right)^{3} + 3 \cdot 2^{\tan{\left(x \right)}} x^{2^{\tan{\left(x \right)}}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) \log{\left(3 \right)} + 3 \cdot 2^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} + \frac{1}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x} - \frac{1}{x^{2}}\right) + \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(2 \right)}^{3} \log{\left(x \right)} + 6 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2} \log{\left(x \right)} \tan{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)} \log{\left(x \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \log{\left(x \right)} \tan^{2}{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(2 \right)}^{2}}{x} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)} \tan{\left(x \right)}}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(2 \right)}}{x^{2}} + \frac{2}{x^{3}}\right) \log{\left(3 \right)}

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Derivada de y=3^x^2^tgx

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Definida a trozos:

Solución