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y=(tg(x))^(x+1)
Derivada de la función/ tg(x)/ (x+1)/ y=(tg(x))^(x+1)

Derivada de y=(tg(x))^(x+1)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   x + 1   
tan     (x)
tan⁡x+1(x)\tan^{x + 1}{\left(x \right)} 
tan(x)^(x + 1)
Solución detallada

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

    Perola derivada

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

  2. Simplificamos:

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-20000000000000001000000000000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
            //       2   \                      \
   x + 1    |\1 + tan (x)/*(x + 1)              |
tan     (x)*|--------------------- + log(tan(x))|
            \        tan(x)                     /
((x+1)(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))tan⁡x+1(x)\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{x + 1}{\left(x \right)}
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Segunda derivada [src] 
            /                                     2                                                           \
            |/        /       2   \              \                  /                           /       2   \\|
   1 + x    ||(1 + x)*\1 + tan (x)/              |    /       2   \ |            2      (1 + x)*\1 + tan (x)/||
tan     (x)*||--------------------- + log(tan(x))|  + \1 + tan (x)/*|2 + 2*x + ------ - ---------------------||
            |\        tan(x)                     /                  |          tan(x)             2          ||
            \                                                       \                          tan (x)       //
(((x+1)(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))2+(tan⁡2(x)+1)(2x−(x+1)(tan⁡2(x)+1)tan⁡2(x)+2+2tan⁡(x)))tan⁡x+1(x)\left(\left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 + \frac{2}{\tan{\left(x \right)}}\right)\right) \tan^{x + 1}{\left(x \right)}
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Tercera derivada [src] 
            /                                         3                              2                  2                          3                                                                                                                                            \
            |    /        /       2   \              \                  /       2   \      /       2   \              /       2   \                            /        /       2   \              \ /                           /       2   \\                                 |
   1 + x    |    |(1 + x)*\1 + tan (x)/              |         2      3*\1 + tan (x)/    4*\1 + tan (x)/ *(1 + x)   2*\1 + tan (x)/ *(1 + x)     /       2   \ |(1 + x)*\1 + tan (x)/              | |            2      (1 + x)*\1 + tan (x)/|             /       2   \       |
tan     (x)*|6 + |--------------------- + log(tan(x))|  + 6*tan (x) - ---------------- - ------------------------ + ------------------------ + 3*\1 + tan (x)/*|--------------------- + log(tan(x))|*|2 + 2*x + ------ - ---------------------| + 4*(1 + x)*\1 + tan (x)/*tan(x)|
            |    \        tan(x)                     /                       2                    tan(x)                       3                               \        tan(x)                     / |          tan(x)             2          |                                 |
            \                                                             tan (x)                                           tan (x)                                                                  \                          tan (x)       /                                 /
(2(x+1)(tan⁡2(x)+1)3tan⁡3(x)−4(x+1)(tan⁡2(x)+1)2tan⁡(x)+4(x+1)(tan⁡2(x)+1)tan⁡(x)+((x+1)(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))3+3((x+1)(tan⁡2(x)+1)tan⁡(x)+log⁡(tan⁡(x)))(tan⁡2(x)+1)(2x−(x+1)(tan⁡2(x)+1)tan⁡2(x)+2+2tan⁡(x))−3(tan⁡2(x)+1)2tan⁡2(x)+6tan⁡2(x)+6)tan⁡x+1(x)\left(\frac{2 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 4 \left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(2 x - \frac{\left(x + 1\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 + \frac{2}{\tan{\left(x \right)}}\right) - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 6 \tan^{2}{\left(x \right)} + 6\right) \tan^{x + 1}{\left(x \right)}
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Gráfico
Derivada de y=(tg(x))^(x+1)
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