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

Derivada de y=(tgx)^(cosx+x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   cos(x) + x   
tan          (x)
tan⁡x+cos⁡(x)(x)\tan^{x + \cos{\left(x \right)}}{\left(x \right)} 
tan(x)^(cos(x) + x)
Solución detallada

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

    Perola derivada

    (x+cos⁡(x))x+cos⁡(x)(log⁡(x+cos⁡(x))+1)\left(x + \cos{\left(x \right)}\right)^{x + \cos{\left(x \right)}} \left(\log{\left(x + \cos{\left(x \right)} \right)} + 1\right)

  2. Simplificamos:

    (x+cos⁡(x))x+cos⁡(x)(log⁡(x+cos⁡(x))+1)\left(x + \cos{\left(x \right)}\right)^{x + \cos{\left(x \right)}} \left(\log{\left(x + \cos{\left(x \right)} \right)} + 1\right)

Respuesta:

(x+cos⁡(x))x+cos⁡(x)(log⁡(x+cos⁡(x))+1)\left(x + \cos{\left(x \right)}\right)^{x + \cos{\left(x \right)}} \left(\log{\left(x + \cos{\left(x \right)} \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-20000000000000000002000000000000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                 /                           /       2   \             \
   cos(x) + x    |                           \1 + tan (x)/*(cos(x) + x)|
tan          (x)*|(1 - sin(x))*log(tan(x)) + --------------------------|
                 \                                     tan(x)          /
((1−sin⁡(x))log⁡(tan⁡(x))+(x+cos⁡(x))(tan⁡2(x)+1)tan⁡(x))tan⁡x+cos⁡(x)(x)\left(\left(1 - \sin{\left(x \right)}\right) \log{\left(\tan{\left(x \right)} \right)} + \frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}}\right) \tan^{x + \cos{\left(x \right)}}{\left(x \right)}
Simplificar
Segunda derivada [src] 
                 /                                                         2                                                                    2                                             \
                 |/                             /       2   \             \                                                        /       2   \                   /       2   \              |
   x + cos(x)    ||                             \1 + tan (x)/*(x + cos(x))|                           /       2   \                \1 + tan (x)/ *(x + cos(x))   2*\1 + tan (x)/*(-1 + sin(x))|
tan          (x)*||-(-1 + sin(x))*log(tan(x)) + --------------------------|  - cos(x)*log(tan(x)) + 2*\1 + tan (x)/*(x + cos(x)) - --------------------------- - -----------------------------|
                 |\                                       tan(x)          /                                                                     2                            tan(x)           |
                 \                                                                                                                           tan (x)                                          /
(−(x+cos⁡(x))(tan⁡2(x)+1)2tan⁡2(x)+2(x+cos⁡(x))(tan⁡2(x)+1)+((x+cos⁡(x))(tan⁡2(x)+1)tan⁡(x)−(sin⁡(x)−1)log⁡(tan⁡(x)))2−2(sin⁡(x)−1)(tan⁡2(x)+1)tan⁡(x)−log⁡(tan⁡(x))cos⁡(x))tan⁡x+cos⁡(x)(x)\left(- \frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 2 \left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \left(\frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \left(\sin{\left(x \right)} - 1\right) \log{\left(\tan{\left(x \right)} \right)}\right)^{2} - \frac{2 \left(\sin{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) \tan^{x + \cos{\left(x \right)}}{\left(x \right)}
Simplificar
Tercera derivada [src] 
                 /                                                         3                                                                                                                    /                                                                 2                                             \                  2                                                        3                               2                                                    \
                 |/                             /       2   \             \                                                           /                             /       2   \             \ |                                                    /       2   \                   /       2   \              |     /       2   \                   /       2   \            /       2   \                   /       2   \                                                     |
   x + cos(x)    ||                             \1 + tan (x)/*(x + cos(x))|                           /       2   \                   |                             \1 + tan (x)/*(x + cos(x))| |                       /       2   \                \1 + tan (x)/ *(x + cos(x))   2*\1 + tan (x)/*(-1 + sin(x))|   4*\1 + tan (x)/ *(x + cos(x))   3*\1 + tan (x)/*cos(x)   2*\1 + tan (x)/ *(x + cos(x))   3*\1 + tan (x)/ *(-1 + sin(x))     /       2   \                    |
tan          (x)*||-(-1 + sin(x))*log(tan(x)) + --------------------------|  + log(tan(x))*sin(x) - 6*\1 + tan (x)/*(-1 + sin(x)) - 3*|-(-1 + sin(x))*log(tan(x)) + --------------------------|*|cos(x)*log(tan(x)) - 2*\1 + tan (x)/*(x + cos(x)) + --------------------------- + -----------------------------| - ----------------------------- - ---------------------- + ----------------------------- + ------------------------------ + 4*\1 + tan (x)/*(x + cos(x))*tan(x)|
                 |\                                       tan(x)          /                                                           \                                       tan(x)          / |                                                                 2                            tan(x)           |               tan(x)                      tan(x)                         3                               2                                                     |
                 \                                                                                                                                                                              \                                                              tan (x)                                          /                                                                       tan (x)                         tan (x)                                                  /
(2(x+cos⁡(x))(tan⁡2(x)+1)3tan⁡3(x)−4(x+cos⁡(x))(tan⁡2(x)+1)2tan⁡(x)+4(x+cos⁡(x))(tan⁡2(x)+1)tan⁡(x)+((x+cos⁡(x))(tan⁡2(x)+1)tan⁡(x)−(sin⁡(x)−1)log⁡(tan⁡(x)))3−3((x+cos⁡(x))(tan⁡2(x)+1)tan⁡(x)−(sin⁡(x)−1)log⁡(tan⁡(x)))((x+cos⁡(x))(tan⁡2(x)+1)2tan⁡2(x)−2(x+cos⁡(x))(tan⁡2(x)+1)+2(sin⁡(x)−1)(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x))cos⁡(x))+3(sin⁡(x)−1)(tan⁡2(x)+1)2tan⁡2(x)−6(sin⁡(x)−1)(tan⁡2(x)+1)−3(tan⁡2(x)+1)cos⁡(x)tan⁡(x)+log⁡(tan⁡(x))sin⁡(x))tan⁡x+cos⁡(x)(x)\left(\frac{2 \left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 4 \left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \left(\frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \left(\sin{\left(x \right)} - 1\right) \log{\left(\tan{\left(x \right)} \right)}\right)^{3} - 3 \left(\frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \left(\sin{\left(x \right)} - 1\right) \log{\left(\tan{\left(x \right)} \right)}\right) \left(\frac{\left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} - 2 \left(x + \cos{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) + \frac{2 \left(\sin{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \cos{\left(x \right)}\right) + \frac{3 \left(\sin{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} - 6 \left(\sin{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)}}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)} \sin{\left(x \right)}\right) \tan^{x + \cos{\left(x \right)}}{\left(x \right)}
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Gráfico
Derivada de y=(tgx)^(cosx+x)
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