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Derivada de la función/ (tgx)/ y=(tgx)^e^x

Derivada de y=(tgx)^e^x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
        / x\
        \E /
(tan(x))
tan⁡ex(x)\tan^{e^{x}}{\left(x \right)} 
tan(x)^(E^x)
Solución detallada

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

    Perola derivada

    (log⁡(ex)+1)exex\left(\log{\left(e^{x} \right)} + 1\right) e^{x e^{x}}

  2. Simplificamos:

    (x+1)exex\left(x + 1\right) e^{x e^{x}}

Respuesta:

(x+1)exex\left(x + 1\right) e^{x e^{x}}

Primera derivada [src] 
        / x\ /                 /       2   \  x\
        \E / | x               \1 + tan (x)/*e |
(tan(x))    *|e *log(tan(x)) + ----------------|
             \                      tan(x)     /
((tan⁡2(x)+1)extan⁡(x)+exlog⁡(tan⁡(x)))tan⁡ex(x)\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) e^{x}}{\tan{\left(x \right)}} + e^{x} \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{e^{x}}{\left(x \right)}
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Segunda derivada [src] 
             /                                           2                   2                                \   
        / x\ |                /       2                 \       /       2   \      /       2   \              |   
        \e / |         2      |1 + tan (x)              |   x   \1 + tan (x)/    2*\1 + tan (x)/              |  x
(tan(x))    *|2 + 2*tan (x) + |----------- + log(tan(x))| *e  - -------------- + --------------- + log(tan(x))|*e 
             |                \   tan(x)                /             2               tan(x)                  |   
             \                                                     tan (x)                                    /
((tan⁡2(x)+1tan⁡(x)+log⁡(tan⁡(x)))2ex−(tan⁡2(x)+1)2tan⁡2(x)+2(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x))+2tan⁡2(x)+2)extan⁡ex(x)\left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2} e^{x} - \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} + 2 \tan^{2}{\left(x \right)} + 2\right) e^{x} \tan^{e^{x}}{\left(x \right)}
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Tercera derivada [src] 
             /                                           3                       2                  2                  3                                                                            /                             2                                \                 \   
        / x\ |                /       2                 \           /       2   \      /       2   \      /       2   \      /       2   \                              /       2                 \ |                /       2   \      /       2   \              |                 |   
        \e / |         2      |1 + tan (x)              |   2*x   4*\1 + tan (x)/    3*\1 + tan (x)/    2*\1 + tan (x)/    3*\1 + tan (x)/     /       2   \            |1 + tan (x)              | |         2      \1 + tan (x)/    2*\1 + tan (x)/              |  x              |  x
(tan(x))    *|6 + 6*tan (x) + |----------- + log(tan(x))| *e    - ---------------- - ---------------- + ---------------- + --------------- + 4*\1 + tan (x)/*tan(x) + 3*|----------- + log(tan(x))|*|2 + 2*tan (x) - -------------- + --------------- + log(tan(x))|*e  + log(tan(x))|*e 
             |                \   tan(x)                /              tan(x)               2                  3                tan(x)                                  \   tan(x)                / |                      2               tan(x)                  |                 |   
             \                                                                           tan (x)            tan (x)                                                                                 \                   tan (x)                                    /                 /
((tan⁡2(x)+1tan⁡(x)+log⁡(tan⁡(x)))3e2x+3(tan⁡2(x)+1tan⁡(x)+log⁡(tan⁡(x)))(−(tan⁡2(x)+1)2tan⁡2(x)+2(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x))+2tan⁡2(x)+2)ex+2(tan⁡2(x)+1)3tan⁡3(x)−4(tan⁡2(x)+1)2tan⁡(x)−3(tan⁡2(x)+1)2tan⁡2(x)+4(tan⁡2(x)+1)tan⁡(x)+3(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x))+6tan⁡2(x)+6)extan⁡ex(x)\left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{3} e^{2 x} + 3 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(- \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} + 2 \tan^{2}{\left(x \right)} + 2\right) e^{x} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} + 6 \tan^{2}{\left(x \right)} + 6\right) e^{x} \tan^{e^{x}}{\left(x \right)}
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